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Market accessibility and the entry decision:A theoretical and experimental examination.

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Market accessibility and the entry decision: A theoretical and experimental examination

Kruse, Jamie Lynette Brown, Ph.D.

The University of Arizona, 1988

U·M·I 300 N. Zeeb Rd Ann AIbor, MI 48106

MARKET ACCESSIBILITY AND THE ENTRY DECISION:

A THEORETICAL AND EXPERIMENTAL EXAMINATION

by

Jamie Lynette Brown Kruse

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF ECONOMICS

In Partial Fulfillment of the Requirements For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

1988

THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have read

the dissertation prepared by ____ J_a_m_1_·e __ L~y_n_e_t_t_e __ B_r_o_wn ___ K_r_u_s_e ________________ _

entitled Market Accessibility and the Entry Decision: A Theoretical --------------------~-------------------------------------------

and Experimental Examination

and recommend that it be accepted as fulfilling the dissertation requirement

for the Degree of Doctor of Philosophy ---=~~~~~~--~~------------------------------

Date

Date

Date

Date

Date

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

Dissertation Director Date )

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under the rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgement the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

V. L. SMITH Professor of Economics

Date

DEDICATION

I dedicate this Dissertation to my daughters, Casey and

Gina, who have inspired me in my work at the same time as they have

helped me to remember what is truly important in life.

iii

PREFACE

This Dissertation focuses on the effect entry has on the

organization of markets. Economic theory is certainly a tool of

the examination but the theory is tempered by test in a controlled

laboratory setting. The presentation is in five chapters. The

first chapter introduces the subject matter. The second, third,

and fourth examine specific areas of industrial organization,

namely, contestabi1ity, capacity constrained price competition, and

their predictive power when compared with other paradigms. In the

fifth and final chapter, I summarize and interpret the results. A

complete accounting of all experiments performed is contained in

the Appendices.

I wish to acknowledge the support and assistance of the

faculty of the Department of Economics. I wish to especially thank

Vernon Smith, Mark Isaac, David Conn, Elizabeth Hoffman, Brian

Binger, Bill Sharkey, Stan Reynolds, Glenn Harrison, Ron Oaxaca,

Kevin McCabe, Stephen Rassenti, and Shyam Sunder for suggestions

and ideas that they freely shared. Finally, I would like to

express my gratitude to my husband, Ed, and daughters, Casey and

Gina, for the love and support that has been so freely given.

iv

TABLE OF CONTENTS

LIST OF TABLES . . . .

LIST OF ILLUSTRATIONS.

ABSTRACT ....

1. INTRODUCTION

Page . vii

.viii

.xi

1

2. CONTESTABILITY IN THE PRESENCE OF AN ALTERNATE MARKET: AN EXPERIMENTAL EXAMINATION . . 9

Sustainability and Entry. Laboratory Tests of the Contestable Market Hypothesis Experimental Design . . . . . . . Alternate Market Treatment. . . . Human Subject Buyers vs. Computer Simulated Demand. The Profit Function . Results

.11

.13

.18

.20

.21

.23

Alternate Market .25 Human Subject Buyers vs. Simulated Demand. .28 Profit Polygon. .29 Tacit Collusion. .31

Conclusions. . . . .33

3. BUYER QUEUING RULES IN BERTRAND-EDGEWORTH DUOPOLIES. .36

Literature of Bertrand-Edgeworth Games. Bertrand-Edgeworth Duopoly Model ... Queuing Rules and Nash Equilibria . .

;Experiments and the Nash Equilibrium. Duopoly Queuing Rule Experiments. Results and Discussion. Conclusions . . . . . . . . . .

4. CONTESTABILITY AND EXCESS CAPACITY IN BERTRAND-EDGEWORTH

.37

.40

.43

.50

.51

.58

.64

OLIGOPOLY. . . . . . . .66

Contestable Natural Duopoly Bertrand-Edgeworth and Excess Capacity. Excess Capacity in Experiments ... Excess Capacity Experimental Design . .

v

.66

.68

.71

.72

vi

TABLE OF CONTENTS--Continued

Page

Results of Three Seller Natural Duopoly Experiments .74 Bertrand-Edgeworth Triopo1y Experiments .78 Conclusions .83

5. CONCLUSIONS. .84

APPENDIX A: SELLER PROFIT SPACE .87

Sellers' Profit Space of Chapter 2 Experiments. .88 Sellers' Profit Space of Chapter 3 Experiments. .89

APPENDIX B: AUXILIARY INSTRUCTIONS.

Seller Price Restrictions(Chapter 2). Seller Instructions(Chapter 2). Seller Cost Tab1e(Chapter 3) ..

APPENDIX C: EXPERIMENTAL RESULTS.

LIST OF REFERENCES . . . . . . . .

.90

.91

.92

.93

.94

114

LIST OF TABLES

Page Table

1. Experimental Design and Treatment Pairs .......... 19

2. Price, Profit and Quantity Sold by the Successful Seller in PLATO Posted Offer Experiment P037. 25

3. Theoretical Predictions ..... 57

vii

LIST OF ILLUSTRATIONS

Page Figure

1. Single Product Sustainable Natural Monopoly. 10

2. Buyer Marginal Valuations and Seller Costs 15

3. Profit as a function of Price. 24

4. PLATO Experiment P194. 26

5. Mean Prices, Alternate Market Treatment. 27

6. Mean Prices, Human Subject Buyers vs. Computer Simulated Demand. . . . . . . . . . . . . 28

7. Mean Prices, 25 Cent vs. 1 Cent Increment Rule 31

8. PLATO Experiment P206, Trading Prices. 32

9. PLATO Experiment P2l0, Trading Prices. 33

10. Residual Demand of Random and Value Queues 43

11. Profit Possibilities Under the Value Queue Assumption. 45

12. Profit Possibilities Under the Random Queue Assumption 48

13. Mixed Strategy Distributions Under the Random and Value Queue (capacity - 1/2). 49

14. Efficient Duopoly Market Price 52

15. Average Cost and Demand Curve. 53

16. Contingent Profit Functions for Value Queue Treatment. 54

17. Price Reaction Functions Under the Value Queue. 56

18. Price Reaction Functions Under the Random Queue. 57

19. Contingent Proft Functions for Random Queue. . . 58

viii

ix

LIST OF ILLUSTRATIONS--Continued

Page

20. P245 Random Queue Duopoly 59

21. P248 Random Queue Duopoly 59

22. P249 Value Queue Duopoly. 60

23. Mean Prices with 95% Confidence Interval for Random and Value Queues . . . . 61

24. Actual Distribution of Prices, Random and Value Queue 62

25. Density of Price Observations, Value and Random Queue 63

26. Nash Price Distribution for Different Capacity Levels 69

27. P282 Random Queue, Three Sellers, Alternate Market. 74

28. P279 Value Queue, Three Sellers, Alternate Market. 75

29. Density of Price Observations, Three Seller Excess Capacity Case. ...... . ...... . 76

30. Pooled Mean Prices with 95% Confidence Intervals, Three Seller Excess Capacity Case ........ . 77

31. Average Cost and Demand Curve, Natural Triopoly 80

32. P326 Natural Triopoly . . 81

33. Actual Distribution of Prices, Random Queue 83

34. Experiment P179 95

35. Experiment P18l 96




39. Experiment P2l0 .100

40. Experiment P211 .101

x

LIST OF ILLUSTRATIONS--Continued

Page

4l. Experiment P236 . 102


43. P249 Value Queue. 104




47. P242 Random Queue 106




5l. P276 Random Queue, 3 Sellers, Alternate Market. 108

52. P275 Random Queue, 3 Sellers, Alternate Market. 108



55. P284 Value Queue, 3 Sellers, Alternate Market 110


57. P278 Value Queue, 3 Sellers, Alternate Market: 111


59. P322 Random Queue, 3 Sellers. 112


6l. P327 Random Queue, 3 Sellers. 113


ABSTRACT

The role of market accesibility and entry is the central

theme of this dissertation. Two theoretical models of oligopoly

theory are examined in a controlled laboratory market setting.

Experimental testing of Contestability Theory is extended beyond

the natural monopoly case and a "safe haven" provides subjects with

a viable alternative to the "contestable" market. Evidence

reported supports the conclusion that the contestable market is

robust to the introduction of the alternate market.

The theory of Bertrand-Edgeworth duopoly is explored from a

game theoretic perspective with special attention to buyer queuing

rule assumptions. Experimental evidence underscores sensitivity of

market outcomes to the queuing rule adopted.

The presence of excess capacity relative to market demand

tends to push theoretical Bertrand-Edgeworth equilibria toward

competitive levels. This result is substantiated by experimental

evidence and is independent of the queuing rule assumed. The

similarity between the Bertrand-Edgeworth excess capacity case and

a contestable natural monopoly market is investigated. The

presence of excess capacity/potential entrants is shown to exert

more downward pressure on observed laboratory market prices than

the presence of additional competitors alone. This result is at

xi

odds with the traditional Structure-Conduct-Performance Paradigm.

A herfindahl index calculated from experimental results has almost

no power to predict market outcome.

xii

Chapter 1

INTRODUCTION

The pursuit to identify factors that determine the

characteristics of markets and industries has been an integral part

of EconDmics from its very beginnings. Adam Smith in reflecting on

the self-seeking efforts of individuals, recognized the role that

the market plays in channeling these individual efforts to the

common good of society. Smith characterized five conditions of

competition:

1. The rivals must act independently, not collusively. 2. The number of rivals, potential as well as present, must be sufficient to fa1iminate extraordinary gains. 3. The economic units must possess tolerable knowledge of the market opportunities. 4. There must be freedom (from social restraints) to act on this knowledge. 5. Sufficient tim2 must elapse for resources to flow in the directions and quantities desired by their owners.

During the 19th century, the use of mathematical reasoning

led to a different, essentially structural concept of the efficient

competitive market. The mathematics of the day required a far more

restrictive definition of "competition". For the competitive model

to "work" mathematically, the competitive seller and buyer must

treat price as a parameter. In other words, each market

1

2

participant assumes that his or her own quantity decision has TIQ

effect on the market price. This requires that individual

quantities be an infinitesimal proportion of the aggregate quantity

traded of a homogeneous good. We are left with the requirement

that the perfectly competitive market have an infinite number of

sellers and buyers(thus making it logically impossible to find a

single example of perfect competition in our finite world). This

is traditionally contrasted with a model of the profit maximizing

single-seller market(monopoly). The monopoly has a decidedly less

attractive outcome from a welfare perspective. Over the decades

economists have attempted to devise models of market organization

that capture the salient features of the industries we actually see

operating in our world, namely markets whose buyers and sellers

number one or more and fewer than infinity.

The goal of this dissertation is to explore a subset of the

models of oligopoly theory. I will confine my investigation to two

main branches of oligopoly theory that have received considerable

attention in recent times. They are Contestable Market Theory and

Bertrand-Edgeworth Oligopoly Theory. I will examine the

implications of each of these theories, highlight their common

ground, and experimentally test hypotheses implied by the theories.

William Baumol chose to use his 1981 address as outgoing

President of the American Economic Association as the vehicle for

launching what he called "An Uprising in the Theory of Industry

Structure". Writings by Baumol as well as Elizabeth Bailey, John

Panzar and Robert Willig (1982) present a mathematically rigorous

representation of the contestable market case. Contestabi1ity

Theory is rich in the array of cost functions and product

configurations that it covers. Central to the Theory of

Contestable Markets is the disciplining effect that a potential

entrant can have on the incumbent(s) in a market. If the

3

potential rival can enter and exit cost1ess1y, ilas access to the

same production technology as the incumbent and has identical

access to buyers, then the equilibrium outcome that ensues from

this perfectly contestable market will be efficient. Among the

desirable properties of the equilibrium outcome are zero economic

profits, Ramsey optimal prices, efficient production and market

structure and an avoidance of cross subsidies in pricing, even for

the case of monopoly. Contestabi1ity theory serves to bridge the

gap that was created between mathematical analysis of a competitive

market and Smith's conceptualization of competition.

The most dramatic results of Contestabi1ity Theory are

apparent in the single product natural monopoly industry. By

definition, the natural monopoly firm's minimum efficient scale

exceeds market demand even at prices equal to minimum average cost.

According to the theory, the only sustainable price is that one

associated with zero economic profits. Any other price would allow

a potential competitor to profitably undercut the incumbent. The

successful entrant can costlessly exit before the incumbent can

negate the entrant's profit through retaliatory or even predatory

4

pricing. Chapter 2 is devoted to laboratory tests of

Contestability in the natural monopoly setting. This study builds

upon previous work by Coursey, Isaac, and Smith(1983) and Coursey,

Isaac, Luke, and Smith(l984). Three treatments are tested in a

controlled natural monopoly setting with two sellers. Treatment 1

requires that sellers must incur a 50 cent opportunity cost when

they choose to post a price in the natural monopoly market. This

embodies the notion of a normal rate of return. Previous

experiments assumed a zero opportunity cost of entry. Contestable

market theory is shown to be robust to a change in entry

opportunity cost. Treatment 2 tests the effect on market outcome

of (possibly strategic) human subject buyers vs. demand-revealing

computer simulated buyers. Markets with human subject buyers

demonstrate a faster and more sustained convergence toward

efficient price levels than markets with computer simulated demand.

Treatment 3 restricts sellers' price offers to be divisable by 25

cents. This greatly simplifies the subjects' price decision space.

Additionally, it negates the nonconcavity problem that exists in

the profit relation in other treatments and previous studies.

Experiments that invoke the 25 cent increment rule show more price

volatility and some interesting cases of tacit collusion.

The formal presentation of Contestable Market Theory is a

relatively new development in Industrial Organization, whereas

Bertrand-Edgeworth(hereafter B-E) Oligopoly Theory stems from

initial formulations dating back to the 1800's. B-E firms choose

5

prices and are restricted in the quantity they will produce. This

restriction is embodied either by a rising marginal cost schedule

or by a capacity constraint. When we focus on the single product

case, we can identify a commonality between the predictions of

Contestability and Bertrand-Edgeworth Models. For example, in a

Bertrand-Edgeworth duopoly in which either seller has sufficient

capacity to satisfy demand at any profitable price, the efficient

price will obtain in equilibrium. This equilibrium prediction

corresponds with the efficient price prediction of a contestable

natural monopoly. The two models utilize markedly different

assumptions, thus, the overlap of predicted results creates the

interesting question of which assumptions are behaviorally

significant.

Joseph Bertrand(1883) first proposed a duopoly model of

firms whose decision variable is price for comparison with Augustin

Cournot's(1838) quantity choi~e duopoly model. Bertrand criticized

Cournot's pioneering work on the basis that it lacked a plausible

explanation of price formation. In Bertrand's model, producers

simultaneously and independently choose prices. Demand is

allocated to the lower-price seller who then produces the quantity

demanded at the stated price. Given constant marginal cost,

Bertrand showed that the only equilibrium must be at the price

which equals marginal cost. The motivation for this result lies in

the fact that either seller is capable of producing enough to

satisfy the market. Hence, the lower-price producer serves the

6

entire market and the higher-price producer sells nothing. If a

producer chooses any price greater than marginal cost, its opponent

will undercut by £ and earn a positive profit.

Francis Edgeworth's 1925 critique of Bertrand recognized

that, except in the case of constant marginal cost, there are

serious existence problems when firms produce a homogeneous good.

Edgeworth modified the original Bertrand model to introduce the

possibility of limited capacity. Edgeworth's firms have either

constant marginal cost up to some fixed capacity or strictly

increasing marginal costs. He characterizes a set of demand

conditions in which one firm cannot serve the entire market.

Edgeworth suggests that prices might be expected to fluctuate over

a range whose upper and lower bounds depend on the two firms'

respective capacities. Appealing to a loosely dynamic approach,

Edgeworth envisioned several rounds of price cutting until

prevailing market price hits a trigger price. Given this trigger

price, the opponent firm finds quoting a high price more profitable

than undercutting the trigger price. Without the threat of being

undercut, the low price firm will subsequently raise its price.

This is then followed by another round of price cutting. The high

price and the trigger price, as described, form the upper and lower

bounds of the Edgeworth range.

Game theorists now recognize that Edgeworth described a

case in which no pure strategy equilibrium exists. There is,

however, a Nash equilibrium in mixed strategies. Bertrand-

7

Edgeworth games, in which capacity-constrained firms choose prices,

have commanded considerable recent interest. Chapter 3 introduces

the Bertrand-Edgeworth Game and demonstrates the sensitivity of

it's theoretical predictions to the choice of buyer queuing rule.

A group of laboratory experiments is reported in which two

different buyer queuing rules are compared. The Value Queue

assumes that single unit buyers queue up with highest-reservation

price buyers first. This is analogous to allocating demand by

running "down the demand curve". The second queuing rule tested,

called the Random Queue, assumes that single unit buyers are

randomly arranged in the queue. All other variables are controlled

across the two treatments. The results under the two queuing rule

assumptions are significantly different, with the random queue

markets sustaining considerably higher prices.

In B-E models using either queuing rule, both firms'

individual capacity and total "market" production capacity as well

as their relationship to aggregate demand, determine the nature of

the Nash equilibrium prediction. In some caSes, B-E models run

contrary to the traditional Structure-Conduct-Performance Paradigm

that has been central to industrial organization policy and

empirical work. Under this paradigm, causality starts with the

market structure representing some measure of the size of the firm

or coalition of firms relative to the entire market. The relative

size of the decision making body then determines the effectiveness

of behavioral strategies or conduct. Market performance as

8

measured by allocative and production efficiency is the end result

of the causal flow. This causality implies an inverse relationship

between the number of firms and the pricing efficiency of the

market. Chapter 4 reports experiments designed to gauge the effect

of number of sellers and capacity/demand relationships on market

outcome. The results are compared to discover which of the

determinants described above exerts a stronger influence on pricing

efficiency. Markets in which there is sufficient productive

capacity that the highest price firm will sell nothing if the other

firm(s) price efficiently show strong convergence to a

competitive-type equilibrium. Also, as the number of firms

increases from 2 to 3, market prices tend to be lower. However,

the presence or absence of over-capacity is the dominant effect.

Chapter 5 will provide a brief concluding statement of the

contribution of this body of research to the fields of industrial

organization and experimental economics. I propose directions for

future research that stem from results reported in the following pages.

CHAPTER 2

CONTESTABILITY IN THE PRESENCE OF AN ALTERNATE MARKET: AN EXPERIMENTAL EXAMINATION

The theory of contestable markets as developed by William

Baumo1, John Panzar and Robert Wi11ig(1982) describes a market with

perfect freedom of entry and exit. Though the theory covers a

broad range of cost structures and production configurations, this

chapter is devoted to tests of contestabi1ity theory as applied to

single product sustainable natural monopolies. In a sustainable

natural monopoly industry, minimum efficient scale exceeds market

demand. Figure 1 depicts the cost-demand relationship

characteristic of the single product sustainable natural monopoly.

The application of Contestable Market Theory to the natural

monopoly industry yields striking results. A single natural

monopolist can produce and sell more efficiently than any

multiple; however, in the absence of potential entry, there is no

incentive for this firm to do so. If only one firm does exist,

that firm has the greatest potential for profitable exercise of

monopoly power. In other industries, the possibility of losing all

of one's customers to active rivals serves to discipline a firm's

pricing behavior away from monopoly levels. According to

Contestabi1ity theory, the disciplining force that pulls market

prices toward efficient levels may come from potential as well as

9

10

active rivals. Thus if entry and exit are costless, even an

unregulated monopolist has an incentive to price efficiently.

Price

Demand

Average Cost

o Output

Fig. 1. Single Product Sustainable Natural Monopoly

In this chapter, I will discuss the concept of

sustainability, previous entry treatments, and the effect of sunk

costs on equilibrium outcome. A survey of the initial experimental

tests of Contestability Theory is followed by the description of my

experimental design and discussion of the results.

11

Sustainability and Entry

The theory of sustainabi1ity was developed by Baumo1,

Bailey, and Wi1lig(1977) and Panzar and Wi11ig(1977). A natural

monopoly is said to be sustainable if there exists a price and

output such that entry by rival firms is unattractive, while all

demand is satisfied and revenues cover total costs of production.

Definition: A natural monopoly with cost function C and market

demand D is sustainable if there is a price p and output q such

that

(i) q - D(p),

(ii) p.q - C(q),

(iii) p~q'<C(q') for all p'<p and all q'<D(p').

In other words, a profit maximizing potential rival sees no

opportunity for positive profits due to entry so long as the market

incumbent chooses a sustainable price and quantity. A sufficient

condition for sustainabi1ity is that average costs of production

fall as output expands. By producing the total market demand, the

monopolist can achieve an average cost that is at least as low as

any potential rival. However, if average costs first fall and then

rise with output, the natural monopoly need not be sustainable as

demonstrated by Sharkey(l982). So by restricting ourselves to

natural monopolies represented by Figure 1, we will examine the

predictions of Contestabi1ity Theory for sustainable natural

monopolies. As stated previously, the Theory of Contestable

Markets relies on cost1ess entry and exit. If some barrier makes

12

entry or exit costly, then the nature of the sustainable price

quantity pair changes, moving further away from the efficient pair.

Early arguments by Bain(1956) and Sylos-Labini(1962) assume that

price is uniquely determined by market demand and a potential

entrant expects the incumbent to maintain preentry production

levels. Under this scenario, the scale economies characteristic of

a natural monopoly would constitute a barrier to entry.

Demsetz(1968) argues that if a potential entrant could replace the

incumbent, then high fixed costs that create economies of scale do

not constitute barriers to entry. In contrast, sunk costs do

create entry barriers even under the Demsetz assumption as

demonstrated by Spence(1977). For any given project or expenditure

of funds, the sunk cost is defined as the difference between the ex

ante opportunity cost of the funds and the value that could be

recovered, ex-post, if the project is terminated.

The need to sink funds into a new enterprise, whether into

physical capital, advertising, or anything else imposes a

difference between the incremental cost and the incremental risk

that is faced by an entrant and an incumbent. Obviously, entry

yields a nonnegative expected profit only if the profits weighted

by the probability of success outweigh the unrecoverable entry

costs that will be lost in the event of failure. Thus for any

industry characterized by positive sunk costs, if entrants face a

nonzero probability of failure then the sustainable price quantity

configuration involves a positive profit to the incumbent(s).

13

Laboratory Tests of the Contestable Market Hypothesis

Previous experimental testing of contestability theory

focuses on a sustainable natural monopoly industry. Coursey,

Isaac, and Smith (1983) produced the initial laboratory tests of

the Contestable Market Hypothesis under zero sunk costs using a

posted offer mechanism on the PLATO computer system. The PLATO

posted offer program allows buyers and sellers sitting at

individual terminals to make exchanges for a maximum of 25 periods.

Each buyer (seller) has a record sheet which shows a marginal

valuation (cost) associated with each unit that she consumes

(produces). Buyers have capacity to buy up to five units of the

homogeneous commodity. Sellers in the contestability experiments

have a capacity to produce and sell up to ten units. The sequence

of events in a single period of a PLATO experiment is as follows:

1. Subject sellers are asked to post a selling price and a maximum quantity (number of units in stock). The price and quantity chosen may be changed any number of times at the subject's discretion.

2. Once satisfied with the price and quantity chosen, the subject seller presses an "offer box" on the touch sensitive screen to irrevocably place his(her price on the market.

3. When all sellers have made a price quantity offer, all sellers' prices are displayed on the terminals of all buyers and sellers. The quantity offered remains private information.

4. Buyers are randomly assigned to a queue and are allowed to purchase one at a time.

5. As each buyer's turn comes up, she may choose not to buy or may choose to purchase units by touching the "price box" on the screen of the seller from whom she wishes to purchase.

6. When buyers have purchased all of the u~its a given seller has in stock, an "out of stock" display repla,:es that seller's price box.

7. After all buyers have had an opportunity to pULchase, the current trading period is closed. Each seller's (buyer's) record sheet is updated to record the period's sales (purchases) and associated subject profit.

8. A new pe~iod begins.

The costs parameterized in my experimental study and in

14

previous work are those of a natural monopoly. Figure 2 shows the

marginal and average costs of a typical seller and the aggregate

demand which comprises individual buyers' marginal valuations.

Appendix A contains sellers' profit space for all feasible price

and quantity combinations. Either of two identical firms can

accommodate the entire market demand at the competitive quantity of

10 units. In the event that both firms match prices, substantial

losses will occur at prices close to the competitive range.

CIS found support for the strong version of CMH in four of

their six duopoly experiments. The remaining two experiments

showed significant convergence of price and quantity toward, but

did not enter the competitive range. CIS also compared the results

of their six laboratory duopolies with four laboratory monopoly

experiments. All experiments utilize human subject buyers on the

demand side of the market. The markets with two sellers show

qualitatively more "competitive" results than the single· seller

markets. Clearly, the presence of additional potential sellers

causes markets to tend toward competitive price levels. This

seminal work was followed by Harrison(1984), Harrison and

McKee(1984) and Coursey, Isaac, Luke and Smith(1984).

$6 r- Demand

$5

$4

$3

$2

$1

I

'--""'"1. •• _. _. I

• .. -.. -·-· .. ·:·:..:.:.:.·:.·:t .. ~~-~ ... -.. ~ ! -. ---"1. - - - - - to ____ "' ____ _ ................... • ~ .1------.-.. -.~.---~- . -----

Average Cost ............ ···L .. _· .. t ......... .

Marginal Cost JI""-'-'"

$o~------~------~I------~--------~------+--------024 6

Quantity 8 10

Fig. 2. Buyer Marginal Valuations and Seller Costs

Harrison(1984) noted several areas in which the original

Coursey, Isaac, and Smith experiments depart from the Theory of

Contestable Markets as described by Baumol, Panzar and

15

Willig(1982). The lively discourse between the authors raised an

issue that is pertinent to the entire field of experimental

economics. Every experimental economist must decide "where to

start" in a study. We are equipped with some 200 years worth of

theory intended to explain the workings of the world. This theory,

16

adheres in varying degrees to the standards of "good" economics.

It should capture the driving forces which organize the economic

behavior of decision making entities in addition to being logically

consistent and mathematically complete. Often, a theorist must

trade-off salient features of a model to gain ~athematical

tractability or certain restrictive assumptions are drawn for the

sole purpose that they facilitate a determinate solution. The

issue becomes whether the experimental economist should perform a

strict test of the theory as stated using the same information

states, etc. where possible or test the predictions of the theory

in a richer environment similar to one in which policy based on the

theory will be applied. I propose that both types of experiments

are important and should be performed and labeled accordingly.

The original set of contestability experiments reported by

Coursey, Isaac and Smith attempted to capture the essence of the

theory in a more general laboratory market setting than that

described by the theory. Harrison's criticism of this study

focused on the sequence in which information is revealed to

subjects stating that the fact that the incumbent and potential

entrant must post prices and quantities simultaneously puts the

Coursey, Isaac and Smith operationalization at odds with the

theoretical models. Harrison reports a set of experiments in which

the incumbent and potential entrant move sequentially. Using what

Harrison calls the Bertrand/Nash assumption, the potential entrant

knows the incumbent's posted price before making the entry(pricing)

17

decision. Harrison reports the results of four experiments which

he calls "an exact operationalization of the theoretical model

proposed by BPW"(Baumol, Panzar and Willig). Three support the

strong version of the Contestable Market Hypothesis as described by

Coursey, Isaac, an~ Smith. The subjects in the fourth experiment

use the sequential information to coordinate a profitable

collusive arrangement. Harrison also reports tests of

contestability with three potential sellers in a market that will

accomodate a single seller and finds that increasing the number of

potential entrants puts additional downward pressure on price.

Nevertheless, Harrison did not provide an "exact

operationalization" of Baumol, Panzar and Willig's theoretical

model either. Panzar and Willig(1977) state:

Since the entrant's products or services are assumed to be perfect substitutes for those of the monopolist, a potential ambiguity arrises if the entrant were to set his price for service i, p.e, equal to the monopolist's price,

m ~ Pi ;i.e. how would the demand, Qi , be split? The natural treatment would require the entrant to actually beat the monopolist's price before he receives any customers. Thus e m when, foreexam~le, we say p S P , the reader may take us to mean p S P - E.

Harrison handles matched prices by randomly choosing a seller to

service the market at the (matched) price which does not reflect

what Panzar and Willig clearly state.

Harrison and McKee(1984) contrast contestability with

various regulation schemes and offer their tests of the

sustainable natural monopoly market using computer simulated demand

for comparison with the Coursey, Isaac and Smith experiments that

18

used human subject buyers. Such a comparison is inappropriate

since Harrison and McKee lacked adequate facilities to perform a

controlled test of the effect of human subject buyers vs. computer

simulated demand.

Coursey, Isaac, Luke, and Smith extend testing of

contestability theory to a market characterized by sunk costs. As

the theory predicts, the laboratory market price, quantity, and

efficiency are not as close to the competitive range as the

outcomes of markets with zero sunk costs. They discuss the effect

of human subject buyers vs. computer simulated demand but used

parameters that differed in absolute terms across the treatment so

did not provide a clean test.

Experimental Design

The present experimental study focuses on three areas of

interest which are briefly described below and expanded in sections

2, 3, and 4. An alternate market with certain payment is

operationalized in the first treatment of the experimental design.

This "safe haven" affords a place from which hit-and-run entry can

occur and establishes $0.50 per period as the normal (competitive)

profit that is the opportunity cost of entry. A second question

addressed in this series is that of the effect on market outcomes

of human subject buyers as compared to demand fully revealed by

computer simulation. The third treatment attempts to test the

effect of restriction of seller offers to those divisible by $0.25

19

on market outcomes. The described $0.25 increment rule restricts

the sellers' decision space and concavifies the otherwise jagged

profit relation. Nine experiments are conducted under a partial

factorial design. Table 1 identifies the experiments by their

PLATO Posted Offer number and describes the treatments exercised in

each.

Table 1. Experimental Design and Treatment Pairs

Experiment Alternate Simulated Offer Market Demand Restriction

CIS Mean NO NO NO

P237 NO YES NO

P236 YES NO NO

P1B1 YES YES NO

P194 YES NO YES

P179 YES YES YES

P211 NO YES NO

P207 YES YES NO

P210 NO YES YES

P206 YES YES YES

20

Alternate Market Treatment

The essence of the "story" of a contestable market is that

an incumbent seller is only safe from hit-and-run entry if he keeps

his price offers so low that the resulting profit yields a rate-of

return that is consistent with that being earned in other

industries. The Coursey, Isaac, and Smith, Harrison and McKee and

Harrison experiments implicitly assumed a normal rate-of-return of

zero.

The alternate market treatment allows potential entrants

access to a safe haven with a risk-free normal profit of $0.50.

Potential entrants must forego the $0.50 opportunity cost to enter

the "contestable" market with its associated risks. For the case

of a natural monopoly with two potential sellers, there is no

equilibrium in which two sellers simultaneously serve the market

profitably. In fact, if price matching market splits do occur,

given the parameters used, substantial losses may be sustained by

both sellers. The Coursey, Isaac and Smith(1983) experiments, with

a high incidence of profit destroying market splits, can be

interpreted as examples of destructive competition. A stable

equilibrium must, therefore, involve one seller choosing not to

enter a competitive bid. A common characteristic of the Coursey,

Isaac and Smith(1983) experiments is that they closely resemble a

special case (n-2) competitive market where "possession" of the

market can change nearly every period. In theory, if profits in a

21

competitive market fall short of a normal return, some of the

participants will choose to pull their resources out of production

of the good and seek another industry in which at least a normal

rate-of-return is possible. The alternate market treatment is

constructed so as to provide experimental sellers with the option

of choosing to leave the contestable market in favor of a safe

haven in which a normal rate-of-return is defined as $0.50 per

period. A supplemental instruction sheet is given to sellers

informing them of the alternate market and the rate-of-return

available in that market. The instruction sheet includes a table

in which subjects record each period the alternate market is used.

A sample of the instruction sheet used for this treatment is in

Appendix B. The procedure for entering the alternate market is to

post a price of $0.00 and quantity in stock of 0 units. Buyers

would then receive an "out of stock" message on their screens from

this seller. The action required to enter the alternate market

involves hitting the same number of keys as to post a price to the

contestable market. Experiments P18l, P206, P207 and P236 offer

sellers the option of an alternate market. These experiments are

paired with P237, P2l0, P2ll, and are also compared with the CIS

results.

Human Subject Buyers vs, Computer Simulated Demand

Coursey, Isaac, Luke and Smith (1984) present the first

comparison of human subject buyers with computer simulation of

22

demand. The comparison of human subject buyers vs. computer

simulation programmed to fully reveal demand has been a topic of

discussion in Coursey, Isaac, Luke and Smith(1984) and in Harrison

and McKee(1984). Coursey, Isaac, Luke and Smith recognize the

effect of under revelation of demand on industries with decreasing

average costs. Buyers can effectively discipline the seller by

withholding demand. In the natural monopoly case, this hits

sellers in their most profitable units. In the Coursey, Isaac and

Smith design a one unit under revelation of demand reduces profit

as much as $1.20 per period. In the Coursey, Isaac, Luke and

Smith study, six experiments are conducted with human subjects as

buyers and six with computer simulated demand. PLATO simulation

of demand is struc tured such that, from the sellers' point of view.,

the time frame is the same whether human experimental subjects or

computer simulation is used to create the demand side of the

market. The only difference, of course, is the possibility of

human error and the potential for strategic withholding of demand.

In the Coursey, Isaac, Luke and Smith study, contrary to

expectations, the presence of human buyers results in a stronger

degree of convergence to a competitive price range. All 12

experiments use the same parameters in terms of deviation from the

identified competitive price. However, the absolute competitive

price is $3.28 for all six human buyer experiments and one of the

simulated demand experiments, whereas the remaining five with

simulated demand use an absolute competitive price of $4.38.

· .

23

Harrison and McKee(1984) criticize the use of human subject

buyers advancing the argument that strategic buyer behavior is

something that we can and should control for in laboratory

experiments. This argument begs the issue. Experimental evidence

reported here and in Coursey, Isaac, Luke and Smith demonstrates

that the presence of human subject buyers does make a difference.

The fact that the theory does not consider strategic behavior of

buyers is a weakness of the theory that the experimental evidence

simply points out. Harrison and McKee lack the hardware (and

software) to run an unbiased test of the effect of human subject

buyers. The present treatment is designed to offer such a test.

In my experimental series, two human subject buyer experiments are

performed, Pl94 and P236. These are paired with Pl79 and Pl81

respectively. Also, P237 is paired with the means of the original

Coursey, Isaac and Smith experiments. All other relative and

absolute variables are the same between pairs.

The Profit Function

Recent contestable market experiments (Coursey, Isaac, and

Smith(1983), Coursey, Isaac, Luke and Smith(1984), Harrison and

McKee(1985), Harrison(1984» have all had a common design feature,

namely a marginal cost structure that yields decreasing average

cost over the relevant range. Tha relationship between profit and

price does not approximate a smooth function in the experimental

setting of PLATO. The combination of this cost structure with a

24

step function induced demand curve leads to a profit relation as

characterized in Figure 3. Given that profit maximization remains

the assumed motivation for sellers (and buyers), this profit

relation could confound subject sellers in their search. Consider

the trading periods 7-12 in CIS (1983), P037 reported in Table 2.

Though prices were relatively stable (within a range of $.10),

profit levels fluctuate widely for prices which deviate only a few

cents from $4.99 (which yields a local profit maximum of $2.92).

SaUer Profit $5~------------------------------------------~

$31----

$2 ./' ............ /. __ ..

$1 .-- .. --.- -- -.--... ----.------------.-... -.---.-.... ---.-.. ----... ---.. -.... --.----... -. -.-.--.. - .-.-

$O~+-----~--------~------~--------~----~~

o 0.5 1 1.6 2 2.e

Price in Deviation from AC< 10) Fig. 3. Profit as a Function of Price

A method of making the profit function concave is

operationalized. This treatment restricts the prices that sellers

are allowed to offer by requiring that they be divisible by 25

25

cents. Sellers are given an additional sheet of instructions

explaining the offer restriction. Appendix B contains a copy of

the auxiliary instructions. The basic struccure of this laboratory

market is the same as that in Coursey, Isaac, and Smith, with

identical parameters in most of the experiments. The rest of the

experiments use parameters that shift the profit function down by

approximately $.40. Posted offer experiments P179, P194, P206, and

P210 include the seller offer restriction. These are paired with

P181, P236, r207, and P211 respectively. All prices are reported

in deviation from AC(10).

Table 2. Price, Profit and Quantity Sold by the Successful Seller in PLATO Posted Offer Experiment P037.

Period Price Quantity Profit

7 5.05 7 2.10 8 4.99 8 2.92 9 5.00 7 1.25

10 4.95 8 2.60 11 5.00 7 1.25 12 5.00 7 1.25

Results

Alternate Market

The presence of the alternate market in which participants

can earn some positive profit with certainty is effectively

incorporated in sellers' decisions in the PLATO market. The

alternate market is offered in six experiments and is used an

average of eight periods during the course of a typical experiment.

It also affords a safe haven from which entrants can hit-and-run.

26

Fig~re 4 shows an example of hit-and-run entry by seller B.

Seller B uses the alternate market extensively throughout the

course of the experiment and in period 11 enters the market,

undercuts the incumbent and escapes to the alternate market again.

Also in period 17, seller B leaves the safe haven and undercuts the

incumbent to take the market. Prices in the experiments without

the alternate market are reported in deviation from AC(lO).

Prices for the experiments that include an alternate market are

reported in deviation from [AC(lO) + $0.50/10] to reflect the

$0.50 opportunity cost.

S8

$6

Pm $4

$3

$2

$1

$0

Trading Prloe

-

1

I!

'- i- '-

8

I!

0 I!

E E 0

0

- I! ~ 0 ,Ii - E - -

-- - '--- '--'- '-

10 18

Trading Period 20

III A Seiling Price 0 B Seiling Prtce o Uneuooeuful Otfer

E denotes eXIt to Alternate Market

Fig. 4. PLATO Experiment P194

Price In deviation. from Min At; 27

Pm Pm

$1.0 _._--_ .... _--_ .. _----_ .. _--_ .. _ ... __ .. _-_._ ........... _ ... _-.••.... _--_._--_._-_ .......

'0.8

$0.0 o

~.~ /~'i\. ~*~~2~ "Ii r . .

'-..",

6 10

Trading Period 16

--*- AI.mats Marlatt -Eo- No Alternate Marklet

Fig. 5. Mean Prices, Alternate Market Treatment

Po

20

Mean prices of the experiments in the two treatment groups

are illustrated in Figure 5. Eight experiments are paired

according to the alternate market treatment variable and are tested

using a t test for two dependent samples. With a t statistic of

1.597, the hypothesis that the mean prices for the two treatments

are equal cannot be rejected at the 5% significance level. A

Wilcoxon nonparametric test for paired samples yields similar

results. An F test on the population variances yields a test

statistic of 1.378. We cannot reject the hypothesis that the

population variances are equal.

28

Human Subject Buyers vs. Simulated Demand.

Strategic withholding of demand by subject buyers can

seriously erode the profits of sellers, particularly if their cost

structure is characteristic of a natural monopoly. When seller

strategies are the area of interest, simulation of demand makes an

increase in the number of replications possible with the same total

money allocation for subject payments. This experimental series

yields three pairings for evaluation of the effect of simulation of

demand versus human subject buyers. Figure 6 contains the mean

prices resulting from the two treatment groups.

Price In deviation from Min AI;

Pm Pm

".0 .. __ .................. _, .. _._ .... _ .... _ .. _._.H ..... ____ .. __ .. __ -_._ ... _ ............... __ .. __ .-.. _ ...... __ ..... __ .. _-_._- ....... --.. ---.---.-.. - ... -...... - ..

$0.0 '--_____ ....L..-_____ .....L... _____ --'-_____ ---'Po

o 6 W W ~

Trading Period --*- HumllUl Subject Buyer. -&- S4mulatttd Demand

Fig. 6. Mean Prices, Human Subject Buyers vs. Computer Simulated Demand

29

We can reject the null hypothesis that mean prices are the

same across the two treatment groups in favor of the alternate

hypothesis that prices are lower with human subject buyers. A t

test for dependent samples is used with a 5% significance level.

Also, the Wilcoxon nonparametric test for paired samples yields the

result that we" can reject the hypothesis that the prices arise

from the same distribution.

Profit Polygon

The method used to smooth the profit function, restriction

of seller offers to those divisible by $0.25, has some additional

effects on seller behavior which were not foreseen before

experiments were actually performed. First of all, the restriction

on prices simplifies the seller's decision space. Previously, over

the range of prices from $0.00 to $2.50, a seller had 250 different

price offers that could be chosen. This decision space shrinks to

10 possible price offers under the price restriction treatment. In

and of itself the simplification of the decision space is not a

particularly bad consequence of the treatment. In fact, it may

help subjects sort out strategies in especially complicated

experiments. However, when the cost structure is that typical of a

monopoly, there is a potential problem. Under the decreasing

average costs of a natural monopoly, if sellers match prices and

share the market, this can result in substantial losses ($2.00 or

more per period for both sellers) when prices are near the

30

competitive range. The reduction of allowable price offers

increases the probability of sellers matching prices by a factor of

25. Since there are market forces pushing seller price offers

toward the competitive price, the probability of loss generating

splits is even higher than splits at other prices. Subject seller

reaction to these loss producing splits is hard to predict. The

reaction to suffering a loss can result in sellers offering higher,

lower, or the same price in the following period. Examples of all

three of these reactions can be found in the reports of individual

experiments contained in Appendix C. A different cost structure

which does not produce losses at matched prices may be the place to

ascertain the effect of smoothing the profit function.

The mean prices of experiments with the price restriction

compared to those without are shown in Figure 7. Note the $0.25

increment group prices show more "noise" than its comparison group.

The hypothesis that mean prices for experiments with the 25 cent

increment rule are the same as the prices of experiments without

this restriction cannot be rejected on the 5% significance level.

Also, a Wilcoxon nonparametric test yields the result that we

cannot reject the hypothesis that the prices arise from the same

distribution.

31

Prloo In deviation from MIn ~

Fmr---------------------------------------__________________ ~pm

".0 . -' .. --....... -.~~.-.---.. ---.-.-.~ ..... -.-------... -.. -. __ ..... _---_ .......... __ .. _._._-_ .......... .

$0.15 t----'\:------:f---

$0.0 L---------L...-------I _____ ..L-____ --L---1Po

o 10 18 20

Trading Period -60- 1 Cent Increment ~ 28 Cent Increment

Fig. 7. Mean Prices, 25 Cent vs. 1 Cent Increment Rule.

Tacit Collusion

The simplification of the price decision space by the $0.25

increment rule allows sellers to identify alternative strategies.

P206 and P2l0 in Figures 8 and 9 both illustrate examples of the

two sellers managing to work out collusive arrangements that

increase profit. P206 has an alternate market treatment and $0.25

increment rule. The sellers work out a market swapping arrangement

of alternating high and low prices in periods 9 through 15, then

the same market swapping arrangement is maintained by taking turns

dropping to the alternate market for the remaining periods of the

experiment.

32

Prloe Offer $8~-----------------------------------------------'

1------~~~~~~--~--~~_,r_----------------------_1Pm

o

~.--------------------------------------------------~~ ... Alt. Mkt. A B B B I!J A B A '8~~~~~~~~~~~~~~~~~~~~~~~

1 10 15 20 25

Trading Period o A Price or .. r ~ B Price Offer

Fig. 8. PLATO Experiment P206, Trading Prices

P210 also has the $0.25 increment rule but no alternate

market. In this case, seller B experiences very low profits during

the initial periods of the experiment. She then attempts to

signal, starting in period 5, but is ignored by seller A. In

period 16 she starts giving very strong signals and seller B

finally responds. This arrangement is not as smoothly cooperative

as the collusive arrangement generated in P206. Se1~er B tends to

occasionally "cheat" on the arrangement.

33

Price Offer .10~~---------------------------------------------'

$9

$8

$7

$3ULJ-~L-~~~-L~J-~~~~-L~~~~~~~

10 16 20 26 1

Trading Period A Price Offer - B Price Offer

Fig. 9. PLATO Experiment P2l0 Trading Prices

Conclusions

The goal of this experimental study is to test two

questions of experimental methodology and examine seller

performance in a contestable market with positive opportunity cost

of entry. For the case of seller price restrictions the series

yields some interesting results. The restriction of sellers'

offers which shrinks the decision space may allow sellers to more

easily look for alternative strategies like the collusive

arrangements discussed in section 4 of the results. Future

34

research with seller price restrictions should include other cost

structures in which matched prices are not so damaging to seller

profits.

The results from this series in comparing human buyers with

simulated demand complement those found by elLS (1984). The

presence of human subject buyers tends to discipline the sellers.

Prices converge toward competitive levels more quickly. This

implies that experimental results that converge to competitive

levels under simulated demand are robust. The addition of human

buyers would tend to reinforce the forces already present.

Secondly, these results emphasize the necessity that complete

theoretical models include both sides of the market.

The addition of an alternate market which induces a

positive opportunity cost of entry is an important contribution.

The safe haven provides a base from which hit-and-run entry is

observed, yet the adjusted market price outcomes are not

significantly different from those in the zero opportunity cost-of

entry case.

The next step for contestabi1ity should be an examination

of market performance under other cost structures and a multiple

market setting. A proposed design will give each experimental

subject seller access to two PLATO terminals. Each terminal will

display the seller's cost structure in a particular market. There

will be a natural monopoly, a potential duopoly, and a safe

alternate market with various entry requirements. The natural

35

monopoly has decreasing average costs over the relevant range so

that any single seller can service the entire market. In the

potential duopoly, firms have identical classic textbook U-shaped

average cost curves. The relationship of firms' costs to demand is

such that two firms can efficiently accommodate demand at a

sustainable price close to competitive levels. Entry conditions

for these two PLATO markets are affected by the rules governing

payments in the safe haven. Issues of cost complementarity and

economies of scope will be accessible under the mUltiple market

design.

Chapter 3

BUYER QUEUING RULES IN BERTRAND-EDGEWORTH DUOPOLIES

This study evolved from what was intended as a set of

baseline experiments initiated in February 1986 to be used for

comparison with a more complicated mUltiple market design (see

IIExperimenta1 Tests of the Contestable Market Hypothesis in a

Multiple Market Setting: A Research Proposa1,11 December 1985).

After the first baseline experiments yielded unexpected results,

more attention was given to the question of buying urder. The

PLATO posted offer market allows purchasing by one buyer at a time

and randomly assigns buyers to the queue. Independent of my

experimental exploration of the effect of buyer queuing,

theoretical developments in oligopoly modeling were also moving

toward a realization of the importance of buying order.

In this chapter, I will discuss recent contributions to B-E

oligopoly theory with particular attention to the buyer queuing

rules assumed. My presentation of a basic model of B-E duopoly

includes a description of the three classes of Nash equilibria ,that

arise from different capacity/demand relationships. This is

followed by an analysis of buyer queuing rules and their effect on

Nash Equilibrium predictions of the model. A description of B-E

experimental work is followed by my experimental design and

discussion of results.

36

37

Literature of Bertrand-Edgeworth Games

A majority of recent papers on B-E Oligopolies utilize

either of two main queuing rule assumptions. The queuing rule

specifies the order in which buyers whose reservation values

represent the demand curve are allowed to purchase one or more

units. One queuing rule, hereafter the value queue, allocates

demand by "marching down the demand curve". Under the value queue,

highest reservation price units go to the lowest-price seller.

There are two constructs on the microeconomic structure of demand

that may be used to generate the value queue. First, consider a

society of n (homogeneous) consumers with identical downward

sloping demand curves. Each customer must be limited to purchase

the same fraction (k./n) of the low-price firm's capacity. l.

Another approach is to consider market demand as the summation of

inelastic demands of heterogeneous customers, each wishing to

purchase one unit of the good provided the price is below his/her

reservation price. Under this construct, the value queue is

generated by ranking the buyers according to their reservation

value and allowing highest reservation values to be first in line.

The random queue has also been used extensively in the

literature. For the homogeneous customer case, the random queue

would occur if customers are allowed to make unlimited purchases on

a first-come first-served basis. The low-price firm's stock could

well be exhausted before all customers have an opportunity to

purchase. The random queue will arise in the heterogeneous

38

customer case when prospective buyers are randomly assigned to the

queue. The low-price firm would serve a random sample of the

population.

Shubik(l959) discusses the structure of a Bertrand

Edgeworth game and three candidate queuing rules which give rise to

different contingent demand for the high-price firm. Martin

Beckmann(l965) chose one of Shubik's suggested rules, a random

queue, and explicitly calculated mixed strategy equilibria for an

example with two symmetric capacity-constrained firms and

normalized linear demand. For explanatory purposes, identify the

amount, a as market demand when p-unit cost c. Beckmann showed

that when each firm's capacity is 1/4 a, the B-E Nash equilibrium

is in pure strategies at the monopoly price. When each firm has

capacity equal to at the pure strategy B-E Nash equilibrium is at

the efficient price (equal to unit cost)-. No pure strategy

equilibrium exists for capacities between 1/4 a and a. For this

case, Beckmann solves for the mixed strategy equilibrium

distribution. Levitan and Shubik(l972) use the value queue in a

model with symmetric firms and linear demand. Additionally, they

look at the case in which at least one firm has sufficient capacity

to supply the entire market. The value queue assumption simplifies

the process of solving for mixed strategy distributions. Levitan

and Shubik show that a pure strategy Cournot solution exists for

identical capacities of 1/3 a and demonstrate the pure strategy

"price-unit cost" equilibrium when each firm has a capacity equal

39

to a. For capacities between 1/3 a and a, only mixed strategy Nash

equilibria can be found.

Osborne and Pitchik(1986) prove existence and uniqueness

for a more general model that includes the one described by Levitan

and Shubik. They permit firms with different capacities and assume

only that demand is continuous and decreasing. Their propositions

include one that equilibrium prices are lower the smaller is

demand relative to capacity. Dasgupta and Maskin(1986b) establish

general existence of mixed strategy equilibria in the Bertrand

Edgeworth model using existence theorems for discontinuous games

developed by Dasgupta and Maskin(1986a). Maskin(1986) presents

existence results for models with production in advance that do not

require symmetry and permit cost functions that are continuous,

nondecreasing, concave or convex, and equal zero when there is no

production. Maskin(1986) also proves existence when production is

to order for strictly convex cost functions. Kreps and Scheinkman

study a two stage game and demonstrate that if firms choose

capacity first and prices in the second stage that a Cournot pure

strategy equilibrium obtains (assuming a value queue). Davidson

and Deneckere(1986) show that the Kreps and Scheinkman(1983) result

crucially depends on the the queueing rule adopted and describe a

numerical method of calculating for the mixed strategy price

distribution in the two stage game with a random queue assumption.

Allen and Hellwig(1986) concentrate on market perf~rmance

in Bertrand-Edgeworth games when the number of sellers becomes

40

large. With their random queue assumption, though the mixed

strategy distributions converge toward the efficient price as the

number of sellers gets large, there is still a positive probability

that some seller will name the monopoly price. Vives(1986) shows

that the supports of the mixed strategy equilibrium do converge to

the competitive price as the number of firms gets large under the

value queue (which he calls a surplus maximizing rule for reasons

not clear to me).

Bertrand-Edgeworth Duopoly Model

The following model represents a simple version of the

Bertrand-Edgeworth game that is similar to those presented in

recent studies of capacity-constrained price-setting firms.

There are two firms and no potential market entrants. Firm

i has capacity ki and kl~k2>0. The total market capacity is

k-kl +k2 . Each firm can produce the same good at the same constant

unit cost, c~O up to its capacity. Given the prices of all other

goods, the aggregate demand is represented by the mapping D:R+~R+.

Let p denote the excess of price over unit cost and let S-[-c,oo].

Define d:S~R+ by d(p)-D(p+c); d(p) is the aggregate demand for the

good when its price exceeds the unit cost by p.

The function d is assumed to be continuous and decreasing

on (-c,PO) where a PO exists such that d(p)-O for P~PO>O and d(p»O

for P<PO' This implies that profit, pd(p) attains a maximum on S.

41

Customers will try, as far as possible to buy the product

at the lowest price. If Pi<Pj' customers buy from firm i until its

supply (k.) is exhausted, then turn to firm j. Assume that when 1

sellers match prices, demand will be divided according to each

seller's capacity. Now we may represent the profit of firm i when

it sets price PiES and firm j sets PjES by

I Li(Pi,ki) if Pi<Pj

hi(Pi,Pj,ki,kj)- ~i(p,ki,k)if Pi-Pj-P

Mi(Pi,Pj,ki,kj)if Pi>Pj

(3.1)

The function Li gives firm i's profit when i has the lowest price.

In this case, firm i will either exhaust all demand at Pi or it

will sell its capacity, ki . Thus

(3.2)

The function ~i represents firm i's profit when i and j match

price. If the price, p, that both firms choose is such that d(p)~k

then both firms will sellout their respective capacities.

Otherwise each will sell some proportion of its capacity. Thus

Firm i's profit in the event that it chooses a price that is higher

than Pj is given by Mi' The nature of Mi depends on the queuing

rule that is assumed. The queuing rule controls the composition of

42

the residual left after the low price firm has sold out its

capacity. Since the possibility of entry is excluded, the high

price seller is in essence a monopolist over the residual demand.

If the residual demand is rich in high-reservation-price buyers,

the firm's profit opportunities are much greater than if only low-

reservation-price buyers are left.

Depending on the relationship of aggregate capacity(k) to

demand, we can identify three regions of interest in terms of Nash

equilibria.

(a) a If aggregate capacity(k ) is less than or equal to the

capacity that a profit-maximizing monopolist would choose, given

demand, then there is a pure strategy Nash equilibrium with both

firms choosing pm, the monopoly price. (For some queuing rules,

this type of pure strategy equilibrium may be supported by

a aggregate capacities larger than k ).

b (b) There is aggregate capacity(k ) and individual capacities k i

and kj

such that both firms will find the residual demand so thin

that maximizing profit over the residual demand is less profitable

than matching prices. The pure strategy equilibrium will be at the

efficient price p-unit cost.

(c) The third region corresponds with aggregate capacity between

a b k and k. In this region, there is no pure strategy Nash

equilibrium. However, a mixed strategy Nash equilibrium exists and

can be determined in many cases. The degree of difficulty

43

associated with solution for the equilibrium distribution of prices

depends on the queuing rule chosen.

Price

d(p)

Fig. 10. Residual Demand of Random and Value Queues

Queueing Rules and Nash Equilibria

The choice of queuing rule affects a seller's profit in the

event that he/she has chosen the highest price. To see this, I

will describe the M.(p.,Pj,k.,k.) function for the value queue and 1 1 1 J

random queue assumption and show how the M. function effects the 1

nature of the Nash equilibrium.

Under the value queue, the highest reservation-price units

go to the lowest-price seller. The residual demand left to firm i

in the event that firm j offered a lower price is given by d(p.)-k. 1 J

44

~nd is represented by GO for the case of linear demand shown in

Figure 10. Note that under this queuing rule assumption, sometimes

called the parallel rationing rule (Maskin, 1986b), the residual

demand curve is determined by a parallel shift of the original

market demand curve inward by kj

(the low price firm's capacity)

Therefore, the high price firm's profit function depends on its

own price choice and the other firm's capacity, which is

parametric. The high price firm's sales will range from 0 to it's

capacity, ki' and will be determined by the residual de manu

function between these two restrictions, thus,

Figure 11 illustrates a duopolist's three possible profit

(3.4)

functions described by (3.1) using the value queue for the case of

linear demand (q-A-p) and symmetric capacities A/2. The linear

portion of Li corresponds with those prices, Pi' such that i sells

out its capacity. The curved portion of Li pertains to the case

where prices are higher than P(ki ). In this case, d(Pi)<ki so firm

i completely satisfies demand leaving no residual buyers for the

higher price seller. Notice that all three coincide at P(k). P(k)

is the price at which demand will accomodate both sellers at their

chosen capacities, kl and k2 '" !.~re.}s no excess capacity at p (k)

nor is there unsatisfied demand.

45

Pro fit (J)

1 2 P(k.) 3 5

Firm i's Price

Fig. 11. Profit Possibilities Under the Value Queue Assumption

Let ~ be the set of cumulative distribution functions in S.

Define Fjf~ such that Fj(p)-prob(pj~p), Define ~ as min supp

Fj(p). This implies that Fj(~)-prob(pj~~)-O. Also define p as max

supp of Fj(p), so Fj(p)-l. The expected profit of firm i for any

price PifS given that firm j chooses prices according to the

distribution Fj is

v Pi v v hi (Pi,Fj ) - J~ Mi (Pi)dFj(Pi ) - Mi (Pi)Qj(P i ) + ~i(Pi)Qj(Pi)

+ fP L. (Pi)dF. (Pi) Pi ~ J

(3.5)

where Qj(Pi ) is the size of the atom (if any) in Fj at Pi' Under

46

v the value queue assumption, the Mi function may be factored out of

the integral since Pj is not an argument of Miv.

v v fPi v fP hi (Pi,F.)=Mi (p.) dFj(Pi)+a·(Pi)[~·-Mi (p.)]+L.(p.) dF.(p.) J 1 E J 1 1 1 1 p. J 1

1

v v - M. (p.)F.(p.) + Qj[~.-M. (p.)]+L.(p.)[l-F.(p.)]

1 1J 1 111 11 J 1 (3.6)

For each capacity pair (k1 ,k2), we can study the price setting game

H(k1 ,k2) in which the strategy set for each firm is ~ and the

payoff function for firm i is h .. A Nash equilibrium may now be 1

defined for H(k1 ,k2) as the pair of distributions (F1,F2)E~x~ such

that for i-1,2

h.(F,F.) :S h.(F.,F.) for all Fd 1 J 1 1 J

(3.7)

The method of solving for the Nash equilibrium relies on the

property of the equilibrium that every price in the support of F. 1

must yield the same expected profit given F .. If some prices J

yielded a higher expected profit than others then (Fl ,F2) would not

be an equilibrium because i could play a strategy which used only

the prices that yield the higher expected profit and reap a larger

payoff. This characteristic is used to "back out" the mixed

strategy solution to the Bertrand-Edgeworth game with value queue.

Since M. is not affected by p., we can identify the maximum of M. 1 J 1,

the maximizer, Pi*' and the associated profit, ITi*' p.* is the max 1

supp of F. since i knows that its opponent will undercut any price 1

greater than Pi* with probability 1. The min supp of Fi is the

price E such that

47

Li(E)-kiE-ni*-hi*(Fi,Fj)

Any price lower than E insures a payoff lower th: '~i*. If Fi and

Fj are atomless, direct solution for F is possible by setting

hi(Pi,Fj)-Eki ·

pki - hi(Pi,Fj ) - Mi(Pi)Fj(Pi) + Li(Pi) [l-Fj (Pi»)

- Li(Pi ) + Fj(Pi ) [Mi(Pi)-Li(Pi »)

- Pi(ki + Fj(Pi)[d(Pi)-kj-ki)

ki(Pi)-P F.(p ) -J i ki+kj-d(Pi)

Solution of the B-E game with random queue is not so

(3.9)

straight forward. The random queue is generated by letting the

fraction of consumers left to the higher priced firm be a random

sample of the consuming population. The expected sales by the

higher-price firm are given by d(P i ) [l-kj /d(Pj ») for Pi>P j .

Refering to Figure 10, the possibilities resulting from a random

assignment of buyers to the queue could range from GD to HF. The

expected residual demand is HD under the random queue.

Firm i's profit given that Pi>Pj under the random queue is

(4.0)

Firm i's expected profit under the random queue is represented by

the following equation.

+ IP L. (p. ) dFj (p . ) Pi ~ ~ ~

functions. r Several Mi

r that the maximum of Mi

curves are drawn for different Pj's.

m m is p for all PjE[P(k),p]. The mixed

48

(4.1)

Note

strategy equilibrium is obtained by solving a set of differential

equations. Davidson and Deneckere(1986) and Beckman(1965) provide

such solutions in each of their models.

Proflt(J)

P(k) 1 2 Pm 3 4 6

Firm i's Price Fig. 12. Profit Possibilities under the Random Queue Assumption

Davidson and Deneckere(1986) assert that the random queue

leads to the best contingent demand curve for firm j. This is true

only when we have a population of identical consumers. If we

49

consider the interpretation of aggregate demand as the summation of

the demands of heterogeneous consumers, then the "best possible"

residual demand curve would be that which allows the low price firm

to sell k. but leaves the maximum number of high value buyers to 1

firm j. (HF in Figure 10)

Davidson and Deneckere(1986) prove that the Cournot-Nash

equilibrium found by Kreps and Scheinkman(1983) is not robust to

any other queuing rule. Krep~ and Scheinkman found a pure strategy

equilibrium in the price stage of a two stage game when Cournot

capacities were selected in the first stage. Davidson and

Deneckere(1986) discuss the same game using a random queue and find

Nash equilibrium in mixed strategies only.

F(p) 1.2

Value Queue

,,/!-~~ Random Queue

1.0

0.8

0.6

0.4

0.2

;I' ;1<"

I

.12 .2 .3

Price .4

Fig. 13. Mixed Strategy Distributions Under the Random and Value Queue (capacity - 1/2)

.5

50

The price distributions in Figure 13 serve to illustrate

the difference in the Nash prediction due to the different queuing

rules assumed. The price distribution functions are the mixed

strategy Nash predictions for the case of constant marginal costs,

linear demand, and symmetric capacities of one half the market

demand at price equal to marginal cost. Firms in the value queue

environment will choose prices equal to or below the min supp of

the random queue distribution with a probability of 0.8. The

experiments that I report desc~ibe a model in which a pure strategy

Nash equilibrium exists when the value queue is used but the Nash

equilibrium exists only in mixed strategies under the random queue.

Experiments and the Nash Equilibrium

Ketchum, Smith and Williams(1984) and Kruse, Rassenti,

Reynolds and Smith(1987) provide initial results as to the

predictive strength of the Nash equilibrium in a laboratory

environment. Ketchum, Smith and Williams(1984) examine two designs

of posted offer markets. In design I, the competitive equilibrium

price is also a pure strategy Nash equilibrium. The competitive

equilibrium price in design II experiments is not a Nash

equilibrium in pure strategies. The resulting market outcomes are

significantly different thus lending support to the Nash

equilibrium concept. Kruse, Rassenti, Reynolds and Smith(1987)

test a four-seller Bertrand-Edgeworth model that is of sufficient

simplicity that an explicit solution of the model is possible.

Kruse, Rassenti, Reynolds and Smith(1987) reject the exact

prediction of the risk-neutral mixed price strategy Nash

equilibrium. Using a Komogorov-Smirnoff test, they reject the

hypothesis that the actual price distribution matches the

theoretically predicted mixed strategy price distribution.

51

However, the Nash prediction does provide the correct qualitative

ranking of the price distributions for the capacities parameterized

and predicts better than all alternative hypotheses. The

experiments I report in the following pages represent a design in

which sellers have U-shaped average cost curves. Due to this

richer design, and discreteness of the parameterization, I can

identify the pure strategy Nash equilibrium for the value queue,

and the min supp and max supp of the mixed strategy Nash

equilibrium for the random queue. The parameterization does not

provide for a tractable solution for the form of the mixed

strategy price distribution.

Duopoly Queuing Rule Experiments

The purpose of the experiments reported in this section is

to determine the effect of buyer queuing rules on market outcomes.

Eight experiments were conducted involving two sellers with

identical cost structures trading in the Plato Posted Offer

Institution with simulated demand. Figure 14 illustrates the

theoretical model I test. Each seller has a U-shaped average cost

curve with minimum at X*. Demand will just accommodate two sellers

52

at the efficient price(P ) that corresponds with AC(X*). Thus the c

efficient outcome involves both sellers producing X* and receiving

P for their output. c

$/unlt

I I

... AC(X)

Pc

Quantity

Fig. 14. Efficient Duopoly Market Price

The laboratory interpretation of the theoretical model is

shown in Figure 15. Each seller has a discrete units version of a

"U-shaped" average cost curve, with minimum at four units. The

market clears with each firm selling 4 units at a price up to $0.15

greater than minimum average cost [ACi (4)]. This yields each

seller a profit of $0.60 per period. In treatment I, fictitious

buyers are randomly queued. Treatment group II buyers are queued

from highest to lowest values (value queue).

$/unlt In deviation from AC(4) $2.5

$2.0 .__--....

$1.5

$1.0

$0.0 ................ II~T?~~

ACl(QI)

1 2 3 4 ! 8

Quantity 7 8

Fig. 15. Average Cost and Demand Curve

53

9

Each subject seller is given a table for calculating total

and average costs from the marginal cost schedule given on the

Plato screen. Subjects are told that demand will be simulated

and, in the event of matched prices, each subject will sell about

half of the quantity demanded at that price. A copy of the

instruction sheet is contained in Appendix B.

Entry costs for additional sellers are assumed to be

infinite. Consequently the duopolists operate in a market with

zero threat of further entry. Each experiment lasts twenty trading

periods, but the end period is not announced. Under the

competitive prediction and assuming zero opportunity cost of

subject time, sellers would cut price to the minimum of average

54

cost, each selling 4 units. The competitive price, quantity and

profit for this experimental design are [$0.00, 8, $0.00].

Collusion by sellers to maximize joint profits would result

in a shared monopoly outcome. A sophisticated version of the joint

profit maximum would result if the two sellers take turns acting as

a monopolist and charge a price of $1.15. This enables the firm

with the low price of $1.15 to sell 4 units and earn a profit of

$4.60. Sellers would have to coordinate a high and low price

pattern to achieve this outcome which yields average profit of

$2.30 per period. A high degree of cooperation is necessary to

achieve this result. Sellers must willingly shut themselves

completely out of the market every other period.

Profit

I 4.6

. '

.15

. ~ ' .

. ' ... L/(pl) .. . - .

\ \

Ir' \ • .' " I . -

\

I~ - _ .... _ .... ~,

,001 ~ . ~. 1111) III) I)))) I) III); 1111; III!!!! I! I!!!! i!!!!!!!!!! 'L:...l

Fig. 16.

p m

Price Contingent Profit Functions for Value Queue Treatment

55

A less sophisticated shared monopoly would result if

sellers match prices at $0.90 and split the market, with an

expected profit of $1.38 per period. The "jaggedness" of the

profit function makes $0.90 the collusive matched price profit

maximum. All of these solutions require cooperation since either

seller can increase profit by undercutting.

So far all hypothetical outcomes result in a uniform price

for this homogeneous product. Therefore the ordering of buyers has

no effect on the predictions. However, if we look at the profit

outcome of one seller's price decision contingent upon the rival's

decision, other strategies become apparent. The contingent profit

functions L. and M. for each seller in the experimental duopoly ~ ~

are illustrated in Figure 16 for the value queue. Notice that the

maximum of the M. function is at the price, $0.15, such that ~

M.($0.15) - L.($0.15). Thus, the Bertrand-Edgeworth Model predicts ~ ~

the pure strategy Nash equilibrium price of $0.15. The price

reaction functions for both firms are illustrated in Figure 17.

The pure strategy Nash equilibrium of $0.15 can be identified as

the intersection of reaction functions.

Firm J'8 Prloe $2.0

$US

$1.0

$0.5

.15

1'-- --- ____ .-&.--..

$0.0 0.15

--------~--------~----------~-----------~

0.5 1 1.6 2 2.5 Firm its Price

Fig. 17. Price Reaction Functions Under the Value Queue

The price reaction functions and contingent profit

functions for the random queue are shown in Figures 18 and 19

56

respectively. Notice that the reaction functions in Figure 18 do

not intersect so no pure strategy equilibrium exists at any price

under the random queue. When its opponent chooses a price of

$0.22, either firm's best reply is to choose the monopoly price,

$1.15. The prices $0.22 and $1.15 form the minimum and maximum in

the support of the equilibrium mixed strategy distribution for

this treatment. The equi1ibrilli~ profit is $0.86.

52.0

$1.5

$1.0

50.6

.22

57

Firm 1'8 Price

$O.O~--------~-------+--~--------~--------~~--------~

o .22 0.6 1 1.6 2 2.6

Firm i's Price

Fig. 18. Price Reaction Functions Under the Random Queue

The Nash equilibrium predicts that value queue treatment

experiments should reach a stahle market price of $0.15. In the

random queue experiments, th~re should be TIQ observations below

$0.22 and more price dispersion. Table 3 summarizes the

theoretical predictions for this study.

Table 3. Theoretical Pr.edictions

Price Quantity Profiti/period Efficiency

Competitive $0.00 8 $0.00 100%

Collusive Sophisticated $0.15 4 $2.30 74% Matched Price $0.90 5 $1. 38 64%

Nash Value Queue $0.15 8 $0.60 100% Random Queue [$1.15,$0.22] [4,7] $0.86 [50%,98%]

Profit

4.6

. LI(pJ)

.....•

Pc a Pm

Price Fig. 19. Contingent Profit Functions for Random Queue

Results and Discussion

The results in this section are based on eight

experiments: four posted offer duopoly markets with a random queue,

and four posted offer duopoly markets with a value queue. Contract

prices are plotted as solid circles and unaccepted offers are

denoted by open circles. Two random queue duopoly experiments are

shown in Figures 20 and 21. In P245 illustrated in figure 20, two

sellers actively compete until period 5. Seller A then offers a

price $1.00 higher than seller B (overshooting what would be the

profit maximum). This market shows no signs of converging to

either the cooperative or the competicive solution. In Figure 21,

prices appear to be cycling and come back up in response to price

signals in periods 4, 5 and 8. Note that each time prices reached

about $0.20 a signal results.

59

Price

I ;;t 3 ~ 5 0 7 ~ 9 10 1/ I~ 13 1'1 /E" lIP 17 It Iq dO 0

0 3.00

Pm • • • •• •• i-- -- -- - - ~ 1-- - -- - - f- - - - -- f-- - - I- -

•••• • ~ ... •

•• •• . ... "

, .. ••• .... • ••• '" •• , .. - OM ~ .. :e ... •••• 1-' .- .... . ...

~ ...... ..... •••• ~ ~-.... -Pe -- -- - f--- i-- - - - - - - -- f-- -- - -- - I- - --

I-- -- f-- -,- - - - 1-- -.-1-- - - 1-- - -- 5 - 1-- -6 7 7 7 5 4 5 6 6 6 5 7 7 4 6 6 5 7 6

Fig. 20. P245 Random Queue Duopoly Price

I :l 3 'f 5 ~ 7 g 9 10 II I~ 13 11 15 110 17 18 1'1 OXJ 0

•

Pm , 1-- - r--- - - -- -- - -- -- - - 1---- I- - 1-- -- -- -..

•• .. .... .... .. , ... u • . ... . .. •• .. ~ ... ~ .. -- ... - 1-" ... ... ... ~ . .... .. ... .... ... .. . . ... ... ~

t!!~- fvu ~.!... -- -- ---- -- -- - - -- - i- - - - - - - -Pe --- - - t- - -- - I- --- - --'- 1-- - - - -- - - r-- -- -

5 7 7 5 4 7 7 5 6 7 6 7 6 7 5 7 7 7 7 7

Fig. 21. P248 Random Queue Duopoly

60

Figure 22 charts the results of a duopoly experiment under

the value queue. This experiment shows the strongest and fastest

convergence to the Nash equilibrium of $0.15 with 8 units traded.

Price

J O!.. j 1 .s ~ 7 g q 10 II IJ. I) '/'1 15 II:; /7 Ig /9 .;1.0

0

Pm

1-- -- -- -- -- -- ---- f-- - -- ---- - - -- -- - -- ---

.... H"--- . .. ~.~~ H _":. .. -- ._- Ht, - ... -.. _ ..... .... ~ .. -- ~'H _,NN I- tIH-- ._. -'-- -- - - -- -- - - -- i- f-- -- - - - - -- -- -- -- ---5 7 7 7 7 7 7 8 8 5 8 8 4 8 5 7 8 8 8 8

Fig. 22. P249 Value Queue Duopoly

The pooled mean prices under the treatments of a random and

value queue are ~~ported in Figure 23. In comparing the results

with the theoretical predictions, we can reject the hypothesis that

the mean price is at the zero-opportunity-cost competitive price of

$0.00 for both the random queue and value queue with t statistics

of 35.17 and 14.43 respectively. Likewise, we can reject the $1.15

sophisticated collusive outcome with t statistics on the order of

-46.52 and -38.57. Also, the collusive matched price joint profit

maximum prediction of $0.90 can be rejected with t statistics of

-28.76 and -27.05 for the random and value queue respectively.

61

PrIce In devIatIon from AC(4)

$08

1 Q

$0.6 [

$0.4

$0.2

$O.O~------~------~--------~-------~------~

o 6 10 16 20 Trading Period

Fig. 23. Mean Prices with 95% Confidence Interval for Random and Value Queues

What is apparent in the figures is borne out by

statistical tests. Using the Wilcoxon nonparametric test for

25

matched pairs, we can reject the hypothesis that the prices for the

treatments came from the same distribution at the 1% significance

level. A t test for dependent samples yields a test statistic of

7.92, again allowing rejection of the hypothesis that the mean

prices are equal in favor of the alternate hypothesis that ranqom

queue duopoly mean prices are greater than value queue duopoly mean

prices at the 1% level of significance.

62

1.0

..---------................ t •• ~-:- ~ _ •• -...,. ~ ..

r----'/ 0.8

................................ ;. 0.8 ..... .,. ,

/ ./ ... _ ..... . 0.4

/ 0.2 ...... / ................................. / .. .

/ ... .. o.o~/~'-L~L-~~--L-~~--L--L~--~~--L-~~--~~~--~~

.15 .5 1.0 1.1 5

Prices Value Queue Random Queue

Fig. 24. Actual Distribution of Prices, Random and Value Queue

Figure 24 shows the distribution of price offers for

periods 16 through 20 in the four random queue and four value queue

experiments. As expected, the value queue experiments have a

greater incidence of low price offers. The random queue prices are

more dispersed and tend to be higher. In fact of the 80

ob:;;ervations from four twenty-period random queue duopoli.es. there

are llQ prices observed at $0.15 or below.

The frequencies of observations from all periods is

illustrated in Figure 25. The median price for value queue

experiments is $0.15, with the p.d.f. skewed to the right. The

median price of the random queue experiments is $0.50. More weight

63

is placed on the monopoly price in the random queue experiments as

would be expected under the Nash prediction. The mean income per

period in the value queue treatment is $.636 which is not

significantly different from the Nash prediction of $0.60. Random

queue sellers did better than the mixed strategy Nash equilibrium

predicts with average profit of $1.03 per period.

Frequency 0.30-

0.26 -

0.20-

0.16 -

0.10 -

0.05 - L. 0.00--0 .1 .2

.. Value Queue . g Random Queue

J Ie -- ~.J .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2

Price

111m] ~

1.3 1.4

Fig. 25. Density of Price Observations, Value and Random Queue

This set of experiments supports the conclusion that the

order of buyers does have a significant effect on market outcomes.

Random queuing of buyers substantially changes the structure of the

Nash prediction. Under a value queue, two of the four experiments

attained the Nash equilibrium of [$0.15, 8, $0.601 with the

64

remaining two outcomes approaching the Nash equilibrium. The

random queue group shows higher price variability and no trading

within the $0.00 to $0.15 range. Mean prices tended to be higher,

although no collusive arrangements are detected.

Recall that these experiments characterize a market that

has the potential for an efficient outcome in which eight units are

traded at a normalized price of up to $0.15. The experiments

reported in this section show that the efficient outcome is not

robust under different buyer queuing 'rules in a duopoly setting.

Conclusions

The accumulation of evidence in this chapter shows that the

impact of different queuing rule assumptions in Bertrand-Edgeworth

models is not trivial. The value queue has often been adopted as a

mathematical convenience in numerous Bertrand-Edgeworth models

including a high proportion of the theoretical pieces cited here.

The theoretical results from these models do not generalize to more

believeable queueing rules. These experiments show the magnitude

by which market outcome can change with a change in the ordering of

buyers.

The Microeconomic constructs that must be used tv generate

the queuing rules studied in this chapter are unsatisfactorily

restrictive. A fruitful avenue for future research is to explore

the equilibria that arise from the value queue and it's mirror

image, the "best" queue. These form the boundaries of all possible

65

buyer arrangements, thus could be used to define the limits of

equilibrium outcomes. Using this approach, we can identIfy those

capacity/demand configurations whose equilibria are robust to

changes in the queuing rule and those that are not. When the

queuing rule does make a difference, the range of equilibrium

outcomes can then be fully described.

The strength of the unique Nash prediction continues to

amass evidence in it's favor. Future directions for further

research include tests of· models in which parameterization permits

the pure strategy uniform price prediction, the pure strategy

nonuniform price prediction, and the mixed strategy prediction.

Such an experimental model will provide a strong test of Nash

theory's ability to organize market outcome.

CHAPTER 4

CONTESTABILITY AND EXCESS CAPACITY IN BERTRAND-EDGEWORTH OLIGOPOLY

My goals in this fourth chapter are: 1) to extend the tests

of the Contestable Market Hypothesis initiated in Chapter 2 to the

case of a contestable natural duopoly, 2) to show that my

contestable duopoly experiments may also be interpreted as the

excess capacity case of the Bertrand-Edgeworth model, 3) show the

common ground occupied by both theories and 4) to report

experiments that separate the effect of excess capacity from

experimental results due to an increase in the number of sellers.

Contestable Natural Duopoly

William Baumol(1982) describes contestable market

equilibria in which the endogenously determined number of sellers

could be 2, 3, etc, " ... suppose two firms can produce the output

vector at a total cost lower than it can be done by one firm or

three firms or sixty or six thousand. Then we say that for the

given output vector, the industry is a natural duopoly." The two

firms in a contestable natural duopoly are forced to price

efficiently due to the presence of potential entrants that will

capitalize on any profit opportunity afforded them by the market

incumbents. Using Baumol's arguments, we can fully describe a

contestable market equilibrium for the case illustrated in Figures

66

67

14 and 15 of Chapter 3 when there are more than two potential

competitors. 'TIle contestable Natural Duopoly prediction

(irrespective of queuing rule assumption) in terms of number of

active sellers, market price, and profit is [2, Pc' 0].

Sharkey(1982) proposes two games as interpretations of a

contestable market. In the first game of n firms with U-shaped

average cost curves, he describes the payoff functions, hi' in the

following way:

For the vector P-(Pl' .... 'Pn) of prices stated by all firms,

hi<P) - 0 if Pi>Pj for some j-l, .. ,n

hi(P) - Pi D(Pi)/k - C[D(Pi)/k] if p ~~; for all j-l, ... ,n where ~is the number of firms choosing the lowest price.

Sharkey finds·that his game generally does not have a pure strategy

Nash equilibrium. This is due to the way in which total demand is

equally shared by all the lowest price firms.

Sharkey then proposes a second game which he calls a

Bertrand-Nash model in which firms are only willing to supply those

outputs which yield at least zero profit. This capacity constraint

also opens the possibility that firms will sell at different (low)

prices. Sharkey also found it necessary to queue the firms based

on some priority ranking. In the case of matched prices,

customers, after a complete search, could purchase only from the

lowest price firm in the front of the queue until its supply is

exhausted. Sharkey's queue of firms, which takes his model closer

68

to previous contestability models serves the same purpose as Panzar

and Willig's(l977) assumption that entrants must undercut the

incumbent by at least £ to gain customers.

Utilizing his second model. Sharkey(l982) proves a set of

propositions for the natural monopoly case. His arguments

generalize to the natural duopoly case.

Proposition 1. If P is an equilibrium price vector for a

sustainable natural duopoly and ~3. then ~i(P)-O for i-l •...• n.

A criticism of Sharkey's characterization of equilibrium is that it

requires at least two firms choose prices for the natural monopoly

case. three firms for the natural duopoly case. and so on. This

does not coincide with the contestable market that Baumol describes

but does lead us toward the excess capacity case of Bertrand

Edgeworth competition.

Bertrand-Edgeworth and Excess Capacity

Levitan and Shubik(1972) and Beckmann(1965) characterize the

variations in Nash pure and mixed strategy predictions as the

symmetric capacities of two firms vary. A common result (though

they use different queuing rules) is that when firms have

sufficient capacity to shut their competitor out of the market at

the efficient price. the Bertrand pure strategy equilibrium (p-c)

emerges. Figure 26 shows the predicted Nash Equilibrium price

distributions under the value queue assumption for capacities

69

ranging from k-A to k-A/3.(where A is the quantity demanded at the

efficient price)

F(p) 1.2

1.0

0.8

0.6

o.~

0.2

o ,1

/ Value Queue A8&umed

~-- .-----;--- ,,-

,- I .'

/ / ;_k-.5A

.2 .3 .4

Price

Fig. 26. Nash Price Distribution for Different Capacity Levels

Osborne and Pitchik(l986) study comparative statics for

capacity variations by one or both firms. Restricting themselves

to the value queue and constant marginal costs, they completely

characterize the Nash equilibrium predictions for a full range of

capacity levels(not necessarily symmetric) and very general demanU

condi tions . They show that the endpoints of the suppo'rts of the

equilibrium strategies are nonincreasing in the capacity of the

larger firm. The endpoints of the supports of equilibrium

strategies increase as the capacity of the smaller firm decreases .

•

70

Quite intuitively, the equilibrium approaches the monopoly outcome

as the smaller firm's capacity converges to zero.

Shubik(1959) shows that as the number of firms is increased

in a Bertrand-Edgeworth market, if ~i~ (where a is defined as

demand at price equal to minimum average cost) and ki~a/n, then the

value of the game approaches that of the competitive equilibrium.

Also, the probability distribution of prices shifts toward the

lower end of the range as n increases. Allen and Hellwig(1984)

show that for a random queue, as the number of firms increases,

Nash equilibria (in pure or mixed strategies) converge in

distribution to a (perfectly) competitive price. However the

supports of the mixed strategy distribution do not converge with

positive weight on the monopoly price even as n~. Vives(1986)

shows that as the number of sellers increase, the supports of the

equilibrium strategies do converge to the unique competitive price

if the value queue is assumed.

My interest is not in the number of firms in the carket but

rather in the level of excess capacity. The papers previously

cited do provide some predictions. For the value queue,

Vives(1986) proves the following proposition for n fir.ms with

symmetric capacities, k , and constant costs. n

Proposition 2.Given n firms in the market and restricting attention

to symmetric equilibria, if k ~a/(n-l) then each firm charges a n

zero price.

This result follows from the fact that firm i can be completely

shut out of the market when the other n-l firms choose a lower

price and thus are capable of supplying the market quantity Q.

71

When we plot the Mi(Pi'~i~j kj ) function, it is a horizontal line

at the zero profit level so the maximum(not unique) will coincide

with P(K) which(in this case) is zero. For the random queue, given

sufficient excess capacity that the highest price firm is thrown

out, the same arguments can be used to predict the Nash equilibrium

price of zero.

Excess Capacity in Experiments

The preceding discussion underscores the fact that a large

proportion of the experiments reported by Coursey, Isaac and

Smith(1983), Coursey, Isaac, Luke and Smitp(1984), Harrison

McKee(1984) and Harrison(1985) cau be interpreted as tests of

Bertrand-Edgeworth competition when there is sufficient capacity to

shut one or more sellers out of the market. Recall that the bulk

of these experiments conform with the zero economic profit

prediction.

Kruse, Rassenti, Reynolds and Smith(1987) report a set of

experiments expressly designed to test the N8.sh prediction in a

Bertrand-Edgeworth(four seller) oligopoly setting. The

relationship of aggregate capacity to demand is a treatment

variable in this study. The population of simulated buyers is held

constant across three levels of aggregate capacity. Treatment I

72

oligopolies have no excess capacity. In fact, there is

insufficient aggregate capacity to satisfy demand at a price equal

to constant marginal cost c. Treatment II experiments test the

case where there is a slight undercapacity at the price equal to c.

Treatment III sellers have an aggregate capacity that is larger

than demand at the competitive price. In this treatment, the

capacity is still not sufficient to shut any seller out of the

market at the competitive price. No pure strategy Nash equilibrium

exists for the capacity-demand relationships characterized by the

three treatments. Kruse, Rassenti, Reynolds and Smith(1987) found

that the risk neutral mixed strategy Nash prediction correctly

organized the qualitative differences in the observed price

distributions arising from the three treatments. As aggregate

capacity increases relative to demand, low prices are observed

with a higher frequency. The experiments I report in this chapter

focus on markets in which there is sufficent excess capacity to

shut the highest price seller out of the market as compared with

markets in which there is no excess or under capacity.

Excess Capacity Experimental Design

Recall the model of the duopoly experiments described in the

previous chapter. lbe treatment operationalized in this study

makes the natural duopoly tested in Chapter 3 "contestable". This

is accomplished by adding an additional potential seller. Instead

of two, there are three potential sellers with identical U-shaped

73

average cost curves. Harket demand will accomodate two sellers at

the competitive price. If all three sellers match price at the

competitive level, they will incur losses. A positive opportunity

cost of entry is induced by providing subjects with a safe haven

that may be chosen instead of the PLATO natural duopoly market.

The return from occupying the safe haven is $0.50 per period.

The experiments reported in this section are parameterized

specifically to reflect the case described by Baumol in which two

firms can provide the output demanded at a total cost lower than

can be done by one or three or sixty firms. The contestable market

hypothesis predicts two firms actively selling at a price equal to

minimum average cost and earning a normal rate of return ($0.50)

each period. The third seller chooses the alternate market in

equilibrium and enters the natural duopoly market only in response

to prices above competitive levels. This prediction is independent

of the queueing rule chosen.

One can identify a sophisticated collusive outcome which

requires that the three sellers take turns charging the monopoly

price of $1.15 in the PLATO market and choosing the alternate

market otherwise. This collusive outcome yields an expected profit

of $1.87 per period. A matched price joint profit maximum yields

an expected profit of $0.70 per period when each seller chooses

$1.15 every period. Of course, cheating on either of these

arrangements yields a higher profit.

Om ..

Pe

74

A qualitative prediction of the Bertrand-Edgeworth model is

that prevailing prices are lower in the presence of excess

capacity. For both the value queue and random queue case, the pure

strategy Nash equilibrium is the same as the contestable market

prediction of [Price, Quantity, Profit]-[$0.125, 8, $0.50]

Price I .;t 3 'f 5 {p 7 8 9 10 1/ J,2 IS 1'1 15 16 17 18 If ~ CJ./ d.o1 .:13 .2'1 $

E E E EE E E E £ E. E £. E E E e. E

- - - 1--- - - -- - I-- - -- - - -- - r- f- -- - - - -- I--- -c ....: .. _ ..

~ , -- - 0

~ -:. ... - ~- -..:. ~ ... _ ... - ~ ~ ~- _ .. be!!: -~ -- I-- -- ~ ~-- - r- --

5- - - -- I-- - - - - -5- 6 "6 f-;.- -.- -7 7 1--

7- -

7 7 7 8 8 4 7 7 7 7 7 7 6 7 7 8 8 7

Fig. 27. P282 Random Queue, Three Sellers, Alternate Market

Results of Three Seller Natural Duopoly Experiments

Eight experiments are reported: four with a random queue and

four with a value queue. Figures 27 and 28 contain representative

experiments for each of the queue treatments in the natural duopoly

design. The random queue natural duopoly shown in Figure 27

attains a relatively stable configuration with one seller in the

alternate market and two sellers in the PLATO market for 11 of the

75

last 12 periods. The prices chosen by the two sellers in the

"duopoly" market hover around $0.15 which is a few cents higher

than the Contestable/Bertrand-Edgeworth prediction. This may be

due to the riskiness of the PLATO market relative to the safe

haven. The value queue contestable natural duopoly experiment

shown in Figure 28 exhibits a stable market configuration at the

market price around $0.125.

Price 1 .:t j 'i ~ lD 7 9 9 10 11 I:J.. 13 1'1 15 16 17 IS Iq ';0 c}'1 ~ ~3 ,).'1 .;IS"

t: E: E E £ E E t: £ E E £ £ £ £ E

c

Pm

-1-- - 1-- -- - - .- -- -- - -I- - - 1-- I- - -- -- - - 1-- -- --

- c • - . -l-

• . . I- ..

.~ .~ - ~~ i-= ~ ..

I-'!!" . -~ I-~ \-'" j;.;'-' \- .' -- I- I-- l- I- ..... J-,-. -00 - 1""""-..... '"" ,.... -Pe

-1-- - -- - 1-- - t- -- \-- - I- --- -- - - 1-- 1-- 1-- 1-- 1-- \-- - -

6 6 7 7 7 7 5 7 7 8 6 6 4 6 7 8 7 7 8 8 8 8 8 7 8

E denotes exit by a seller to the alternate market

Fig. 28. P279 Value Queue, Three Sellers, Alternate Market

Figure 29 shows the frequency of price offers made by all

sellers in the final five periods of the experiments. For both

queues, observations greater than $0.10 but less than or equal to

$0.20 predominate. Notice, however, that more random queue offers

are observed in the higher price ranges. None of the theories

76

predict the observed difference in equilibrium. One factor that

might explain the behavioral difference in markets with identical

equilibrium predictions is that the random queue still yields

higher profits than the value queue for offers above the

equilibrium price.

Frequency 0.8 -

0.6 -

0.4 -

0.2 -

0.0-- L

III Value Queue g Random Queue

~jJi -.mL-EI --0 .1 .2 .3 .4 .6 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4

Price

Fig. 29. Density of Price Observations, Three Seller Excess Capacity Case

The pooled mean prices with 95% confidence intervals are

plotted in Figure 30 for the two queuing rules. Clearly, the

laboratory outcomes allow us to reject both of the collusive

predictions. The markets for both queuing rules seem to be

converging toward the Contestable/Bertrand-Edgeworth prediction.

Though the two queueing rules yield results that are more similar

77

for the excess capacity case than when there is no excess

capacity, they still diverge. According to a Wilcoxon

. nonparametric test, we can reject the hypothesis that the mean

prices arose from the same distribution. The t test for dependent

samples yields a t statistic of 5.56. We may reject the hypothesis

that the mean prices from the two treatment groups are the same in

favor of the alternative that the random queue mean prices are

greater than the value queue mean prices.

o Random Queue v Value queue

Price In deviation from AC(4) $1.0

$0.8

$0.6

$0.4

$0.2

$0.0 L.... ___ -L-___ ...L-___ ..l-. ___ .L-__ ---l ___ --'

o 6 10 16 20 26 30

Trading Period Fig. 30. Pooled Mean Prices with 95% Confidence Intervals,

Three Seller Excess Capacity Case

When the random queue contestable du.!:lpoly results are

compared with the random queue duopoly experiments reported in

Chapter 3, the resulting t statistic is 3.19. We may reject the

hypothesis that the mean prices are equal in favor of the alternate

78

hypothesis that the contestable duopoly mean prices are lower than

the (uncontested) duopoly prices.

When we compare the results from uncontested and contestable

natural duopolies under the value buyer queue, we cannot reject

the hypothesis that the prices arose from the same distribution at

the 5% level of significance. The t statistic of 1.56 conforms

with the results of the Wilcoxon nonparametric test.

One alternate explanation of the results reported in this

section has not been clearly eliminated. Introducing another

potential competitor to the natural duopoly market obviously

increases the number of sellers from two to three. A viable

alternate explanation, in concert with the traditional structure

conduct-performance paradigm, is that the number of competitors has

increased and that, in and of itself, would generate a more

competitive solution.

Bertrand-Edgeworth Triopoly Experiments

The structure-conduct-performance paradigm has been a

mainstay in the study of industrial organization. Under this

research program, a strong causal link has been welded between the

number of sellers in a market and the prices that prevail. The

inverse relationship between the number of sellers and industry

wide profit levels is accepted as a stylized fact in this branch of

industrial organization. A vast body of empirical research is

devoted to exploring the Structure-Conduct-Performance linkages in

79

various industries. Empirical tests require quantification of

industry structure using some measure of the number of firms

present and their size relationship. One well accepted summary

measure is the Hirschman-Herfindahl index, often called the

Herfindahl index and given by:

H-~ s 2 i

where si is firm i's quantity share of total market sales. H

varies from 0 to 1 and tends toward 1 as the number of sellers

decrease and/or are more unequal in size. Thus, one would expect a

positive relationship between H and prevailing market price.

If we accept the hypothesis of the Structure-Conduct-

Performance Paradigm, this would serve as a suitable explanation

for the result reported in the previous section. The experiments

reported in this final section are designed to allow separability

between the effect of increasing the number of sellers and the

introduction of excess capacity.

Smith(198l) reports tests of the effect of increasing the

number of sellers from one to two in a posted offer market. To

isolate the effect of increasing the number of sellers, Smith

replicates both sides of the market by cloning each subject's cost

or value parameters. Merket prices fell with an increase in the

number of sellers from one to two. Smith's experiments represent a

pure scale change while holding the capacity/demand relationship

constant.

80

In the final treatment, I make a pure scale change in the

size of the market, keeping per capita income opportunities

constant. To scale the market up from two sellers to three, a

clone, with cost identical to the other two sellers is added to the

supply side of the market. Since all buyers are not identical,

scaling up the demand side of the market requires that new values

be added to the aggregate demand curve which are equal to the

expected value of one half of the original demand curve. This

preserves the profit-to-price relationship that existed in the two-

seller duopoly experiments. Figure 31 illustrates the costs and

values parameterized in this treatment.

$/unlt $3,Or $2.5

$2.0

$1.5

$1.0

$0.5

Demand

1 2 3 4 6 6 7 8 9 10 11 12 13 14 16

Quantity Fig. 31. Average Cost and Demand Curve, Np.tural Triopoly.

81

If sellers match prices at the shared monopoly price of

$1.15. they can each sell two units for a profit of $1.30 per

period. The capacity/demand relationship is such that no pure

strategy Nash equilibrium exists. The supports of the mixed

strategy prediction are the same as in the duopoly case(as per

Allen and Hellwig(1986» but we would expect higher probability

weight on the lower prices in the support. The minimum and maximum

prices in the support are $0.22 and $1.15 respectively. A

significant positive relationship between the Herfindahl index and

market price would lend support to the Structure-Conduct-

Performance Paradigm.

Price

1 c 2 3 '( 5 b 7 8 9 10 /I 12 13 1'( 15 If) 17 lie 19 20

Pm . ,

c .. .... _. - .... c 0 - c - 1--- -.... ........ .. oJ .. oJ _ . -1-.-- ... .... .... -_. l- I-- . .. ....... . .. -...

I-,... .....

1--"- ~ ..... r--Pe

-- --I-- 1-- - -- -- --- I-- -- -- -- -- -- -- I-- t- -- -- -- - -5 8 8 8 7 9 6 8 8 8 8 8 8 8 9 8 9 8 8 8

Fig. 32. P326 Natural Triopoly

82

Figure 32 shows a representative experiment from this

treatment group. The price pattern in this experiment is

reminiscent of those found in the two-seller random queue duopoly

experiments reported in Chapter 3. Comparing the mean prices of

the random queue duopoly and triopoly experiments with no excess

capacity yields a t statistic of .059. We cannot reject the

hypothesis that the mean prices are equal. The Wilcoxon

nonparametric test supports this conclusion.

The distributions of observed price offers for the duopoly

and triopoly with no excess capacity and the natural duopoly with

excess capacity are shown in Figure 33. Notice that the triopoly

prices are qualitatively more like the distribution of prices from

the two-seller natural duopoly experiments than the three-seller

excess capacity experiments. Apparently, excess capacity

influences the "competitiveness" of the market outcome more than

the number of competitors does. Finally, a Herfindahl index was

calculated for each period of the twelve experiments. A mean

Herfindahl index was calculated for each experiment. A linear

regression was calculated using the mean Herfindahl index

as the independent variable and mean market price as the dependent

variable for the twelve experiments. The coefficient on the

Herfindahl index of .199 is not significant with a standard error

of .507 and a t statistic of .392 . 2 The R for the regression is

. 015 indicating that the Herfindahl index has practically no

predictive power in the controlled laboratory setting of these

experiments.

F(p) 1.2 r

I 1.0 _~ ............ ~~~~ ... _. " ... ~".'='~'~ fJ· ~" .

. / e---~' 0.8 .. ...... ........... >/' ",.- . 'r" ... .

.... l-· .-0.6

1

....... /.~~./.. . ... r·-:~.·<" .' III

0. 4 r···· .. /'-"', ,.' .r··· • /'if /' ... .. ... .. ...... . . ..... -.. -- ... -......... - .. ---. - .

0.2 1-.. --1 ..... - ... /- ............ .... -;1-.. -.......... ................. -....................... -.. -...... -................................... -................... _- ...... .

0.0 I. j tJ,' e.=£.~.' .16 .6

Prices 1.0 1.16 1.6

83

. ~.. 3 Firma No Exceaa 3 Firma Exc8ea Cap. -e- 2 Firma No Excesa

Fig. 33. Actual Distribution of Prices, Random Queue

Conclusions

The experiments reported in this chapter served to "close

the loop" initiated in Chapter 2. The presence of potential

entrants or excess capacity facilitates a competitive-like outcome

even in markets with very few sellers(only one or two active

sellers). Contestability/excess capacity is shown to have a

stronger influence than does increasing the number of competitors.

A naive structure-performance linkage that does not include some

measure of excess capacity or potential entrants has little

predictive power.

CHAPTER 5

CONCLUSIONS

The oligopoly models examined and tested in this study were

initially developed in different centuries. Joseph Bertrand's

1883 model of firms that compete through price has been enriched by

the contributions several generations of economists. This

enrichment of Bertrand and eventually Bertrand-Edgeworth models

epitomizes a progressive research program that moves the science

of economics forward. Contestable Market Theory also builds on

ideas that have existed since Adam Smith. However, the credit for

formalization of the Theory of Contestable Markets must go to

Baumo1, Bailey, Panzar, and Willig for their work in this decade.

This study utilizes laboratory testing throughout as a

fundamental tool to facilitate better understanding of economic

phenomenon. The results of those laboratory tests indicate the

strengths and the weaknesses of the theories tested. Contestable

Market theory does have predictive power at least within the realm

in which it has been tested so far. Some of the assumptions

necessary to make Contestabi1ity theory work analytically are not

required for it to work behaviorally. This is demonstrated by the

first set of experiments performed by Coursey, Isaac, and

Smith(1983). My experiments which induce a positive "normal rate

84

85

of return" through an alternate market complement the results that

preceded them. This indicates that the direction of future

research should extend further into the richer cost and product

environments that Contestability Theory covers.

The behavioral significance of active(human) demand vs.

passively revealed demand is not captured by any of the theories I

examine. The results of my experiments clearly indicate that some

equilibria may be quite sensitive to actively strategic buyers.

The competitive equilibrium for the contestable natural monopoly is

a case in point. This indicates that future theoretical research

should formalize the effect of strategic buyers in market models.

I suspect that the characterization of equilibria will change very

little for some market models, but could be vastly different for

others.

Bertrand-Edgeworth Game-theoretic models are sensitive to

the fairly restrictive assumptions presently being made about the

allocation of demand to sellers with different prices. The

experiments reported in Chapter 3 show the magnitude of differences

that are possible. Game theorists should move toward a more

general characterization of demand allocation or at least

recognize the limitations on the models they presently propose.

Further experimental research should explore proposed game

theoretic equilibrium concepts with particular attention to the

Nash Equilibrium.

Excess capacity is an important determinant of market

performance. The limited tests reported in Chapter 4 show that

excess capacity is more important than the number of active

This

86

Market

competitors in pushing markets toward efficient outcomes.

information should be used in prescribing public policy.

mechanisms that utilize free access to excess capacity can

potentially produce efficient results in lieu of regulation.

Future research should move toward developing and testing such

mechanisms.

My contribution to Contestable Market Theory and Bertrand

Edgeworth Oligopoly has been made primarily through the device of

laboratory tests. Those controlled laboratory tests provide the

yardstick by which the efficacy as well the deficiencies of the

the~ries can be measured. My experiments indicate several fruitful

directions that the next stage should take. In a sense, this

final chapter summarizes important results reported in this body of

work but also provides an introduction to the next phase of my own

research program.

APPENDIX A

SELLER PROFIT SPACE

87

88

SELLERS' PROFIT SPACE FOR CHAPTER 1 EXPERIMENTS

Price 2.36 2.11 1.86 1. 61 1.36 1.11 0.86 0.61 0.36 0.11 Range 2.12 1. 87 1.62 1.37 1.12 0.87 0.62 0.37 0.12 -0.13

Q(P) 1 2 3 4 5 6 7 8 9 10

Profit q.-1 1.24 0.99 0.74 0.49 0.24 -0.01 -0.26 -0.51 -0.76 -1.01

1 1.00 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00 -1.25

q -2 2.23 1. 73 1.23 0.73 0.23 -0.27 -0.77 -1. 27 -1. 77 i 1. 75 1.25 0.75 0.25 -0.25 -0.75 -1. 25 -1. 75 -2.25

q.-3 2.97 2.22 1.47 0.72 -0.03 -0.79 -1.53 -2.28 1 2.25 1. 50 0.75 0.00 -0.75 -1.50 -2.25 -3.00

q.-4 3.46 2.46 1.46 0.46 -0.54 -1.54 -2.54 1 2.50 1.50 0.50 -0.50 -1.50 -2.50 -3.50

q.-5 3.70 2.45 1.20 -0.05 -1.30 -2.55 1 2.50 1.25 0.00 -1. 25 -2.50 -3.75

q .... 6 3.69 2.19 0.69 -0.81 -2.31 1 2.25 0.75 -0.75 -2.25 -3.75

q -7 3.43 1.68 -0.07 -1. 82 i 1. 75 0.00 -1. 75 -3.50

q -8 2.92 0.92 -1.08 i 1.00 -1.00 -3.00

q -9 2.16 -0.09 i 0.00 -2.25

q -10 1.15 i -1. 25

89

SELLERS' PROFIT SPACE FOR CHAPTER 2 EXPERIMENTS

Price 1. 90 1.65 1.40 1.15 0.90 0.65 0.40 0.15 Range 1.66 1.41 1.16 0.91 0.66 _0.41 0.16 -0.09

Q(P) 1 2 3 4 5 6 7 8 Profit q -1 1.15 0.90 0.65 0.40 0.15 -0.10 -0.35 -0.60 i 0.91 0.66 0.41 0.16 -0.09 -0.34 -0.59 -0.84

q.-2 2.30 1.80 1.30 0.80 0.30 -0.20 -0.70 1 1.82 1.32 0.82 0.32 -0.18 -0.68 -1.18

q -3 3.45 2.70 1. 95 1.20 0.45 -0.30 i 2.73 1.98 1.23 0.48 -0.27 -1.02

q.-=4 4.60 3.60 2.60 0.60 -0.40 1 3.64 2.64 1.64 0.64 -0.36

q.-5 3.25 2.00 0.75 -0.50 1 2.05 0.80 -0.45 -1.70

APPENDIX B

AUXILIARY INSTRUCTIONS

90

91

SELLER PRICE RESTRICTIONS

In this experiment, seller prices have been restricted to those divisible by $0.25. If you enter a price that is not divisible by $0.25, then the machine will automatically round your price to the nearest $0.25. You may either use that price or select a different one.

For Example:

If you choose a price of $1.87, your offer will appear as $1.75. You will then be asked to choose a quantity or you may change you price by simultaneously pressing shift and edit.

If you choose a price of $1.88, your offer will be entered as $2.00 and the same procedure as outlined above follows.

92

ALTERNATE MARKET INSTRUCTIONS

As a seller you may choose to enter an alternate market instead of the one on your screen, for which you will receive $0.50 per period. You may do this by selecting a selling price of 0.00

and quantity of O. At the end of the experiment, you will be paid the gross profit from the record sheet on your screen plus total earnings from the alternate market listed in the table below.

Period

1

2

3

4

5

6

7

8

9

10

Participated in Alternate Market

Total periods in Alternate

Market

________ X $0.50 -

Period

11

12

13

14

15

16

17

18

19

20

Participated in Alternate Market

Total Alternate Market Earnings

# of Units Additional Sold Cost

I

2

3

4

5

SELLER COST TABLE

Total Cost

Per Unit Cost (total cost/# units)

93

IN THIS EXPERIMENT, THE DEMAND FOR YOUR PRODUCT WILL BE SIMULATED. IN THE EVENT THAT YOU MATCH PRICES, YOU WILL EACH SELL APPROXIMATELY 1/2 OF THE TOTAL QUANTITY SOLD IN THAT PERIOD.

APPENDIX C

EXPERIMENTAL RESULTS

94

$.8,-----------------------,

I

Pm $4 Pc

10 15

Trading Period Cd Seller A, _ Seller 8 Offer

Fig. 34. Experiment P179

20 26

R Alt MH

95

96

$6,----------------------,

$6

Trading Period DSeller A. _ !?eller 8 • (lffer 1( .A.I t Mk t.

Fig. 35. Experiment P18l

97

$8.---------------------------------------~

:~ Pc

$2 r'~ .. ~

$0 1 ~

r n

. ~~ l I

~ IIII1

10 1':- 20

Trading Period :)f !9r


;f,6,--------------------,

,f.;6 •

Pm' $4 Pc

$2

. ~. ri . i~. ~I' ~i ! I ! I II . ~ II II

~1 ! II 1 t~ t I I

5

I I I I

10 15 20

Trading Period o S811~r A M:::<?lIer 8 • (lffl?r tt to.1 t MI< t.


98

99

Trading Period


100

Trading Period o Seller ,A _ :3eller 8 • I)ffer


10 115

Trading Period


101

I I I I . '. I

, "I ~ I M ~

~ ~ I ~ ~ ~ ~ I ~ ~ R· I t\

102

$8~----------------------------------~

10 15

Trading Period


RI I I

I n I : I

II II r I

20

103

:f.8r------------------,

I $6 . I

P . . $4 .

I ~ n

. Pc

~ ~ .

" ~ .

.. I $2 ~ I I . . I ,. I . I t\ I I I

..

III I I I \ \. $0

.

I~ 1·. . . . rn I

~I~I II~I tJ Ii I .

t\i ! II ~n · '5 10 115 20 213

Trading Period


PC'ice

1.00

.15

.00

Price

1.00

• 15

.00

J <L J 'I S ~ 7 S q

- - -- - -- - - -- -

-f--I'":": _": b:-: r-~ r-":

- - - - - - - 1--S 7 7 7 7 7 7 e 8

Fig, 43.

1 ~ 3 'I C, . IP 1 II 9 10 10·'"

• - - - -- -- -I- -

- .. r' - .... . .. .... 'M' I- r--..

h' .: -.... - - -- - - -- - - -rS -i--

~ 1-4 - 1-.-5 6 6 7 6 7 7

Fig. 44.

10 /I I:" IJ Ii( 15 Ib 17 Ii

- --- I- - -- - -

'r-' i'--1-" I-- I-r-~

~ 1-- - re- - -..: ---e 8 4 S 7 8 8

P249 Value Queue

1/ I~ 13 1'/ 5 i/: '7 18 19

- - - l- .- - - -- -

.. ... -- ~ 1;-... - ~! ... 1--... . ... ~ .. ~ .. ~ ... - 1-- I-S -1-- 1--

7 7 7 4 5 5 7 8

P250 Value Queue

19

-

.10

---

Trading Period

-I-----8

,;0

-

....... 1--

8

8 Quantity Traded

Trading Period

Quantity TC'aded

104

Price

1.00

. 15

.00

I

.

....

-~

d 3

1- -

----

56

I

'/ S 10 7 s 9 10 /I Id.. /3 I'{ IS 1(" 17

,- - r - - ,- - - - -- - - - -

:--N ... ... ... .... "N ... .... "- .. --... . - _.- .. - ..u . .. .....

- -- -- -- - - - - - - -- -- --- - '7 ~ -,- '5 7-6 6 6 7 7 7 7 7 7 7

Fig. 45. P251 Value Queue

5 10 1\ la 13 11 15 Ii

If 19

,- -

_.-I--- ri-7

d ~o

<)0

-

-:."

-7

Trading Period

105

Quantity Traded

d. 3 Ij I; 1 g q 110 17 Trading Price Period

1.00

.15

.00

-.... _ ..

- -

56

-- - -- -- - - , -- o _

. . ...... " N .... r- I~ 'N"

r--' ... .... -" .- ... 1 - .... ... I- UN r-'

• N ... - ,- - - 1-- - -- I-- - ,- - --I- -- - 1--

65 ~ 66 6 6 :) 6' 6'6 77 5 5 74 6

Fig. 46. P252 Value Queue

Quantity Traded

Price

PM 1.00

.15

.00

I ~ 3

0

- --. . .... --

- -

5 5 5

'I '5 II!

I- 1-- f--I

.... . 1'-" ....

- - -

5 6 6

7 g q 10 11 1;1. 13 1'1 15 110 3.~l

r1 I~'

- - I- - 1-- - .- - .- f-- - 1--

. .... • . . . ... f-~ .... .. ... "'M .... ... ...

io •• : ...

~.

- - - -- -f- -- - I- - -

5 5 6 6 6 6 6 6 6 4 6 6

Fig. 47. P242 Random Queue

,q

-

. ~ . ---7

(}O

-

. _ . -

6

.. \

Trading Period

106

Quantity Traded

Price Trading I ;;t 3 J.j 5 0 7 \? q 10 II IJ.. 13 '" IS lIP 17 18 Iq c)D

.15

.00

-

.. ...

1--

6

- -

.. -.... i-- -

7 7

. - -

...... ", ..

--I--

7 5

• l'o c

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10'" . .

•• .. • = ", .. ... ....

.~ - .M ..:0 .... 1-' .- ". " ... - --- - - - - -1-- 1-- - I- -I- -

4 5 6 6 6 5 7 7 4 6 5 6 5 7


-_ .. -

. . .... -

6

Period

Quantity Traded

Pdce

1.00

.15

.00

I .;l 3

-- I-

l-!-. ....

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s s~

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'--

6 6

10 7 K 9 /0 " 1:1. 13 If IS I/' 17 II 19 ",0

- - - - - - - 1--I- --.. .. . .

r" foo .. " joooo' .... !-. .... _ . .. I- - ... .... ....

1--00 '_. 'M'

-I- -I- - -- - t-- - -- -- -I- - -'s '5 6 s 5 6 6 6 5" 6 6 6

1-,

6 66


Trading Period

Quantity Traded

107

I J. 3 '{ 5 r, 7 g 9 10 II I~ 1,3 i1 15 It" 17 18 I~ l-w Price Trading

1.00

. 15

.00

.

1-"

---s

-

.. ... --

7

. - -

... ... N' -- -

7 ~

(

. . - -- - --- r- - - - - I- - I-..

.. .. .... 00 .. ... '" ... .. I ... oo '00-". - 1-' ... 1-' ... ... I- - - - -- -- - - - - -

-~

.. .. - - .. 4 7 7 6 7 6 7 6 7 S 7 7


-- -

....... .... - -,- .. -7 7

-

... .. . -

7

Period

Quantity Traded

108

D '71'; ,., ..

Trading Period

,1., .2 J AI S 6 1 8 9 10 " 12 13 /'1 /5 I~ 17 /I IV ':0 :11 ~ 01' ~ .:15 III E E E E

Price 0

1.00 _1_ - - - -'- - -- -f- - - --- - - -- - - -- -- -

.. .. • . . . , ~"

.;. l-I-" .. , ~

1-0- ~ I- !-oM I-,"- ~ I-~ r-" -:..... .

~ ... r-- ", .. ... H' i-': LJ ... I-" I-"

.15

.00 - - -- -I- .- - -I- -f- -I- - f-- -- - - - - - - - --- -,- - -'-- - l- I- - I- -i- I-- - - - -1-- - - -

14 5 5 6 6 6 5 6 6 6 6 6 6 7 6 7 7 7 6 7 6 7 7 7 7

Quantity Traded

Fig. 51. P276 Random Queue, 3 Sellers, Alternate Market

Trading Period 1 J. 3 ., S " 1 8 9 10

£ £ Price

. . I..., -l- I- - -I- ' -1.00

.. ~ ~ I-1-, 1-' ~~ r-- l- ...

.15

.00 f- .- -- --I-

- - .- - .- -f-- -I-4 5 5 5 5 5 5 5 5 5

Quantity Traded

1/ 12. 13 ,., £ £

-- -

r-- 0

"- ,

I-

,- --f-

- f-- - f--5 5 5 6

I~ II, n 18 19 ~o <11 .:101. :!3 ;,'/ ~s

£ E f£ 300.

-- -- - f-- f- 1-- --I-- f-- 1--,

M

f-• ... "- .. _. -'- - .-~-:.. 10-;-- ,;,.- f;..--- - - - - -1-- - -- -- -6 6 7 7 8 4 8 7 8 8 8


Tradin

Price

1.00

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Penod J .:l .3

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. . M

l- I- -'" -- --

I- - -6 6 7

'f

-

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1--7

Quantity Traded

5

1--

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-7

(, 7 i 9 10 1/ E £ E EE

--I-- -1---- -. .

.o. io-H.

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IA 13 1'1 /5 I~ J7 IS 19 AO ~ I~A ;/3 ~'1

EEt. E

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, . ... . M • ...I -I-~ ~ .. "'" r,..-F-- --I-- - -- .- -- -I-- -1-- - --

8 8 8 4 5 7 7 8 8 7 8 8 8


Tra

Price

1.00

• IS .00

dlng Period I .:I. 3 'I

E

- - - -,

",.J ... " , ..

1-'"

-- .- -- - - 1--5 6 6 7

Quantlty Traded

S fD

- 1--

M, --1--

1-- -7 7

7 8 9 10 111.3. £ £ E£ E

- - 1-- - l- f-

... M .. ......

i-l r:."" l-- '-- - - t- ·5-7 7 8 8 4

13 /'/ IS 16 17 II " .:!O .;)./ dol ~3 :J.'I E E £ £ E E E. £ E E.

-- - - 1-- - I- ,.... 1-- - - - 1--

~

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'.-~ I->- .;;-.~ .or-

- -I- - I- -- I-- - - - -7 7 7 7 7 7 6 7 7 8 8 7


109

"'5 I:

--

--8

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110

Trading Period J :J.. 3 <I 5 " 7

Price q{() E 71XJ 11.00

1.00 - 1-8 - - !- :- -

.15

.00

,.. .. ....

.- --, 44

~ ....

--5

__ .i .... .... ...

-- ,- -- - - l-5 5 5 5

Quantity Traded

.

8 '1 10\ ~ 1:2. 13 1M E

- l- i- - - -. . . ....

1--" .. .... ...... : .... .... -t-- -- --

I- i- - - - -5 5 6 6 5 5

1'/ 15 It" 17 I~ 1'1 :;0 ~I ~ 013 ",1 015 ££ II/)() E 1100 r;. IU~ E. lEE IE '1.0/) 5.S()

IE E Il6b '/.0£ (',D~

l- i- t-- - - - .- --i- -- -I .... . -. ..oo .... .... " . .. .. " i""

.. .. ~!... "" -- - ..... ... - -

l- e...._ - -- -- - -- -- --4 6 6 7 4 7 4 7 4 0 4 5

Fig. 55. P284 Value Queue, 3 Sellers, Alternate Market

Trading Period

1 .:t .3 "I 5 G. 7 Price

1.00 -- - .- - --

.-. ~.~

. -" .... ... " H." .. ~.

.15

.00 i--

I-5

- -,- -5 6

- ----- -l- I-6 6 6 6

Quantlty Traded

8 9 10 /I

'-- - - -

~.- ...... --- -- ~- ........ -- I-- f-- -

7 7 7 8

I;), 13 1'/ /s I" 17 ~l 19 dO :)1 ClO! :3 EIE ~ £ £ E

o

-- -- - -- -- - -- -- - -c

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c

--

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--

;;;.----8

111

Trading Peciod

~;". -:; 3 '( 5 " 7 8 '1 10 II 1:1. 13 /'1 15 '" 17 It 19 ;0 <3.1 -'0:2. ;23 ~¥ .25 E E ~ £ E E E £ E E IE e

price

1.00 I- - -- - -I- -- I-- - - - - i- - --- -- -- -- - - - --

__ I- I- : 1--I-~ 1-. 1--1-.. .. - ~-:: I=-~ ~~ ~ .... - ~. 0- _ -- - 1---~- ~"- f~ I"""' w .15

.00 - - 1-- r- 1-- -- - i-- - 1--1-- - 1-- -- -- -1---

5 5 6 6 7 7 7 7 7 6 7 7 8 8 8 7 8 8 8 8 8 8 8 7 Quantlty Traded


Fi 57 P278 Value Queue, 3 Sellers, Altarnate Market g. .

Trading Period

Price

1.00

.15

.00

I .:t 3 '/ £

-- 0- _ ,

. I-

,

I- -1:=

_o~

--1-- -- -6 6 7 7

~

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-

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Quantlty Traded

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- --

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/I I;J. IJ 1"1 15 Ie 17 18 1'1 £ E E E E E

-- .- - 1-- I- ---

I-=- ~ 1=.' r- ~~ ~., ~ l-I'-O

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-- - - 1-- -- -

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8 8 8 8 7 8


8

112

Trading Period 1 2 3 " 5 b 7 8 9 10 /I Ii!. IJ 11 15

0 '" 17 18 19 20 Price;

. • . 0

~ ..:. -.! . ... -~ ... - ... I- -'" -.... ~ ... i- -! fooo -N' --'" i-......... - ... ... -... --. I- ...

r--Pc

- -- - -- -- -- -- -- --I-- - -- - -- -- - -- -- -- ---7 8 7 8 8 9 9 10 10 8 8 8 9 9 8 8 8 7 8 8

Quantity Traded

Fig. 59. P322 Random Queue, 3 Sellers

Trading Period

Price I, 2 3 'i 5 6 7 F 9 10 /I 12 13 1'1 15 Ib 17 Ii 19 20

, .. ... _. .... ... 0 -- ..: ....... ....... - ... , .... -.. -'- .. - ... . ...... ....... ... ....... .. ._--~ ..... ...

. _-- - - - -- - -- - -- -- - -- -- -- - - .- - -- --5 8 8 8 7 9 6 8 8 8 8 8 8 8 9 8 9 8 8 8

Quantity Traded

Fig. 60. P326 Random Queue, 3 Sellers

LIST OF REFERENCES

Allen, B. And M. Hellwig, "Price-Setting in Firms and the Oligopolistic Foundations of Perfect Competition", American Economic Review Proceedings. May 1986, 76, 387-392.

Bain, J. S., Barriers to New Competition, Cambridge: Harvard University Press, 1956.

Baumo1, W. J., "Contestable Markets: An Uprising in the Theory of Industr.y Structure." American Economic Review March 1982, 72, 1-15.

Baumo1, William J., E. E. Bailey, and R. D. Willig, "Weak Invisible Hand Theorems on the Sustainability of Multiproduct Natural Monopoly," American Economic Review, June 1977, 67, 350-365.

Baumol, William J., Panzar, John C., and Willig, Robert D., Contestable Markets and the Theory of Industrial Structure, New York, Harcourt, Brace, Jovanovich, Inc., 1982.

Beckman, M. J. (with the assistance of Dieter Hochstadter), "Edgeworth-Bertrand Duopoly Revisited," Operations ResearchVerfahren. III, edited by Rudolf Henn, Sonderdruck, Verlag, Anton Hain, Meisenheim, 1965, 55-68.

Bertrand, J., "Review of the Theorie Mathematique de 1a Richesse and Recherches sur 1e Principes Mathematiques de la theorie des Rechesses," Journal des Savants, 1883, 499-508.

Chou, Ya-lu, Statistical Analysis with Business and Economic Applications, New York, Holt, Rinehart and Winston, Inc., 1969.

Cournot, A. A., Researches into the Mathematical Principles of the Theory ofVea1th, New York, Macmillan, 1897.

Coursey, D., M. Isaac, M. Luke andV. L. Smith, "Market Contestability in the Presence of Sunk Entry Costs," The Rand Journal of Economics Spring 1984, 15, 69-84.

Coursey, D., M. Isaac, and V. L. Smith, "Natural Monopoly and Contested Markets: Some Experimental Results," Journal of Law and Economics. April 1984, 27, 91-113.

114

115

LIST OF REFERENCES--Continued

Davidson, C., and R. Deneckere, "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," The Rand Journal of Econohlics, Autumn 1986, 17, 404-415.

Dasgupta, P. and E. Haskin, "The Existence of Equilibrium in Discontinuous Economic Games, 1: Theory," Review of Economic Studies, 1986a, 53.

Dasgupta,P. and E. Maskin, "The Existence of Equilibrium in Discontinuous Economic Games, 2: Applications," Review of Economic Studies, 1986b, 53.

Demsetz, H., "Why Regulate Utilities?," Journal of Law and Economics, April 1968, II, 55-65 .

. Edgeworth, F. Y., Papers relating to Political Economy I, London, Macmillan, 1925.

Harrison, Glenn W., "Experimental Evalutation of the Contestable Market Hypothesis," Working Paper 1984.

Harrison, Glenn W. and Michael McKee, "Monopoly Behavior, Decentralized Regulation, and Contestable Markets: An Experimental Evaluation," The Rand Journal of Economics, Spring 1985.

Ketchum, J., V. L. Smith and A. W. Williams, "A Comparison of Posted-Offer and Double-Auction Pricing Institutions," Review of Economic Studies,1984, LI, 595-614.

Kreps, D. and Scheinkman, J., "Cournot Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, 1983, 14, 326-337.

Kruse, Jamie L., "Experimenta1 Tests of the Contestable Market Hypothesis in a Multiple Market Setting: A Research Proposal," 1L!1publ ished Manuscri.pt, Depar tment of Economics, Univexsity of Arizona, December 1985.

Kruse, J., S. Rassenti, S. S. Reynolds, and V.I. Smi th, "BertrandEdgeworth Competition in Experimental Markets," Discussion Paper No. 87-12, Department of Economics, University of Arizona, November 1987.

116

LIST OF REFERENCES--Continued

Levitan, R. and M. Shubik, "Price Duopoly and Capacity Constraints," International Economic Review, 1972, 13, 111-121.

Maskin, E., "The Existence of Equilibrium with Pric-Setting Firms," American Economic Review Proceedings. May 1986, 76, 382-386.

Osborne, M. J. and C. Pitchik, "Price Competition in a Capacity Constrained Duopoly", Journal of Economic Theory, 1986, 38, 238-260. .

Panzar, J. C. and R. D. Willig, "Free Entry and the Sustainability of Natural Monopoly," Bell Journal of Economics, Spring 1977, 8, 1-22.

Plott, C. R. and V. L. Smith, "An Experimental Examination of Two Exchange Institutions," Revie'tl1 of Economic Studies, February 1978, 45, 133-153.

Scherer, F. M., Industrial Market Structure and Economic Performance. Second Edition, Boston: Houghton Mifflin Company, 1980.

Schwartz, Marius and Robert Reynolds, "Contestable Markets: An Uprising in the Theory of Industry Structure: Comment," America .. Economic Review, September 1984, 74, 572-587.

Sharkey, W. W., The Theory of Natural Monopoly, Cambridge: Cambridge University Press, 1982.

Shepherd, William G., "Contestabi1ity vs. Competition," American Economic Review, June 1983, 73, 488-490.

Shubik, M., Strategy and Market Structure, New York: John Wiley and Sons, 1959.

Smith, V. L., "Induced Value Theory," American Economic Review, 1976, 66, 274-279.

Smith, V. L., "An Empirical Study of Decentralized Institutions of Monopoly Restraint," in G. Horwood and J. Qurik(eds.), Essays in Contemporary Fields of Economics, West Lafayette: Purdue University Press, 1981.

, LIST OF REFERENCES--Continued

Sp&nce, A. M., "Entry, Capacity, Investment and Oligopolistic Pricing," Bell Journal of Economics, 1977, 8, 534-544.

Sylos-Lambini, P., Oligopoly and Technical Progress, Cambridge, Mass.: Harvard U.P., 1962.

117

Vives, X., "Rationing Rules and Bertrand-Edgeworth Equilibria in Large Markets," Economic Letters 1986, 21, 113-116.

Waterson, M., Economic Theory of the Industry, Cabridge: Cambridge University Press, 1984.

Weitzman, Martin L., "Contestable Markets: An Uprising in the Theory of Industry Structure: Comment," American Economic Review, June 1983, 73, 486-487.

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