TOPIC 8: OLIGOPOLY AND GAME THEORY

Topic 8 | Part 2 6 June 2013Date

ANTITRUST ECONOMICS 2013David S. EvansUniversity of Chicago, Global Economics Group

Elisa MariscalCIDE, ITAM, CPI

2

Overview:

Part 1

Role of Oligopolies in

Economy

Game Theory and Strategic

Behavior

Part 2

Oligopoly Theory: Cournot

and Bertrand

Dynamic Games and Competition

3 Oligopoly and Interdependent Behavior

4Oligopoly and interdependent behavior

• Practically, we use this term for cases where there are a handful firms that account for most of the output.

• Oligopoly (like monopoly) requires the existence of barriers that prevent entry or expansion of fringe firms such as economies of scale or network effects.

Oligopoly refers to industries with a handful of firms:

Oligopoly firms can’t act independently of each other.

Any change in price or output by one firm will materially affect the price, sales, and profits of other firms.

Each firm recognizes that the ultimate effect of its decision to change its price or output depends on how other firms react (in particular, do they follow or not?)

5The Role of strategic behavior: key features

• Best action of each particular firm depends upon the action of the other competitors (just like prisoner’s dilemma game).

A key feature of oligopolies is strategic interdependence between competitors:

• BMW, Jaguar, Mercedes. They must consider pricing, styling• Sony PlayStation vs. xBox. They must consider pricing, features,

release dates.

A firm must consider its rivals’ behavior to determine its own best policy or strategy. Consider for instance:

How does this equilibrium change with the number of firms and the type of actions firms may take?

Generally, oligopoly models predict that prices decrease with the number of firms, but the magnitude of the price decrease varies greatly depending on the assumptions.

6Oligopoly models and their different assumptions

• Price—that is, the announce price and sell what people will buy at that price. OR

• Quantity—that is, the offer a quantity and take whatever price they can get in the market to absorb that quantity.

Models assume that firms focus their conjectures on:

• Static—firms move simultaneously and the game is over in the blink of an eye; like deciding which way to move when two people are walking into each other on the sidewalk. OR

• Dynamic–firms move sequentially like in chess; models must assume who goes first.

Models assume something about timing:

7Basic Cournot model for two-firms: assumptions

Two firms in a market for a homogeneous product (spring water)

Firms make output decisions simultaneously instead of choosing prices.

Each firm independently attempts to maximize profits by choosing its output based on its conjecture about the other firm’s choice

Linear market demand and constant marginal cost as shown.

Price

D(P)

PA

D(PA )

A possible price that firm A might consider

The market demand schedule

The quantity firm A would sell if firm B supplied nothing.

Q

MC

Marginal revenue

8

Firm A’s decision based on its conjecture about how much firm B will offer

If Firm A believes Firm B will produce q1

B ,what is Firm A’s optimal quantity?

If Firm B produces q1B , Firm A will

be facing a “residual demand” dA(qB)=D(p)- q1

B

Market demand

Residual demand for Firm A if Firm B sells q1

B

Price

D(P)

Q

MC

q1B

9

Firm A’s profit-maximizing output given firm B’s output decision

Firm A will set marginal revenue equal to marginal cost, given residual demand

If Firm B produces q1B then Firm A’s profit maximizing output is q1A

Price

MC

Residual demand for Firm A when Firm B

produces q1B

MR for Firm A given its

residual demand

q1A

Price

D(P)

Q

MC

q1B

10

Firm A’s decision on how much to supply varies with its conjecture about firm B’s supply

Note that when qB=0, the residual demand for Firm A equals the market demand

Hence, the optimal quantity chosen by Firm A is that of a monopolist: qM

A

Price

Q

MC

q1B

D(P)

Residual demand for Firm A when Firm B

produces q1B

MR for Firm A given its residual

demand

q1A

11

The “best response curve” summarizes A’s best moves for each of B’s choices

For each value of qB, Firm A has a Best Response based on its maximizing profits rule.

We can write down a schedule of these “best responses” for Firm A for every possible output by Firm B. This is called Firm A’s “Reaction Function” or “Best Response Function”.

The reaction function is key for analyzing the equilibrium decisions of oligopoly firms.

12

The reaction function is linear when demand Is linear

For a linear demand function and constant marginal cost, the reaction function will also be linear.

q2Bq1

B qB

Firm A’s Reaction Function

qC

qMA

qA

q2A

q1A

Firm A produces the monopoly level when firm B produces nothing

Firm A supplies nothing to the market if Firm B supplies the entire market (by pricing at marginal cost—i.e., the competitive level) since it can’t make any profit.

13

Firm B also has a reaction function based on a similar analysis

Firm B has a similar reaction function that shows its best response, given what Firm A chooses.

Under the assumption that both firms have the same marginal cost Firm B’s reaction function will be identical to Firm A’s.

Note Firm A and Firm B’s reaction functions are being drawn from different orientations (i.e. B on the horizontal axis is looking at what A on the vertical axis is doing; while A on the vertical axis is looking at what B on the horizontal axis is doing.

qA

Firm A’s Reaction Function

q C

q M

q M

q C

Firm B’s Reaction Function

qB

14

The Cournot equilibrium occurs where the reaction functions cross

• Each firm has chosen the profit-maximizing quantity given their conjecture about what the other firm is doing (so the equilibrium is on the reaction functions);

• Each conjecture is right in that each firm correctly anticipates what the other does.

The “equilibrium” is at the intersection of the two reaction functions and where:

Proof: At any other point on the reaction functions at least one firm is wrongly anticipating what the other will do.

Firm A’s Reaction Function

qCB

qMA

qMB

Firm B’s Reaction Function

Equilibrium

qCOURNOTB

qA Verify for the Cournot output it is less than the competitive level but greater than the monopoly level.

qCA

qCOURNOTA

Total output = 2 x qCOURNOTA,B = qCOURNOT

A +qCOURNOT B

15

With Cournot oligopoly, total price is more than with competition but less than with monopoly

In Cournot equilibrium, market price is lower than what a monopolist would charge but higher than the competitive one.

Deadweight loss is also lower than that in the monopoly case in the same market, but still positive.

qC

D(P)

COMPETITION

COURNOT

MONOPOLY

QQ COURNOTqMA,B

MC

P

PM

PCOURNOT

16Introduction to the Bertrand model

Forty-five years after the publication of Cournot’s book, Joseph Bertrand (1874-1900) observed that Cournot’s results depended on the assumption that firms compete over quantities. [ See Bertrand, J. "Theorie Mathematique de la Richesse Sociale," Journal des Savants, 67, 1883, pp. 499-508]

Bertrand considers what happens if the firms’ “strategic variable” consists of prices instead of quantities. (Do you think firms are more likely to play price or quantity; does it depend on the features of the industry?)

Bertrand’s model adopts the same assumptions as Cournot theory except the strategic variable is price instead of quantity.

17

Firm A’s decision based on its conjecture about firm B’s price

Products are perfect substitutes: Whichever firm charges the lowest price gets all the sales.

If price set by Firm A (PA) is lower than price set by Firm B (PB), Firm A’s demand will be D(PA)—the market demand—whereas Firm B’s demand will be zero. And vice versa.

If both Firms set the same price P= PA= PB then each Firm will get half of the demand: ½ D(P) (assumes customers choose randomly since firms are identical).

D(P)PA

QA =D(PA < PB) Q

PB

Firm B charges a higher price but gets

zero demandP

18The Best Strategy with Bertrand Competition

If Firm A conjectures Firm B will set monopoly price its best price is slightly below that then, it gets all the monopoly profits for itself.

If Firm A conjectures that Firm B will set price between competitive and monopoly price, its best price is again slightly below It doesn’t get all the monopoly profits but at least it gets all the profits available at this supra-competitive price.

If Firm A conjectures that Firm B will set price at competitive level its best price is also at the competitive level (equal to marginal cost) It loses money at a lower price and makes no sales at a higher price.

Firm B is symmetric to Firm A and behaves exactly in the same way.

19Equilibrium with Bertrand competition

The equilibrium is where price equals marginal cost (the competitive level).

At any higher price the conjectures are inconsistent. Whatever price a firm expects, the other one will undercut it to get the whole market and the entire profits.

At the competitive price firms cannot cut prices any more because they will lose money (does predatory pricing make sense here?). And they cannot raise prices either because they will lose all sales.

So at P = MC conjectures are consistent with each other: if Firm A charges the competitive price, Firm B will too, and vice versa.

20Bertrand model with product differentiation

As the number of competitors goes from one to two, the equilibrium price goes from the monopoly level to the perfect competition price.

The Bertrand model assumes both firms sell identical products.

With slightly different products undercutting the rival’s price the model does not guarantee a firm gets the entire demand.

With differentiated products equilibrium price is above marginal cost.

Differentiated-market Bertrand accords with reality and this model is extensively used in econometric studies of markets and in merger analysis.

21

Cournot and Bertrand can both be restated as games

The Cournot and Bertrand equilibria are Nash Equilibria in non-cooperative games.

Bertrand is an example of a prisoner’s dilemma game where the players independently choose the worst possible outcome.

Cournot is an example where the players in the end could have done better or could have done worse.

22

Oligopoly theory and the embarrassment of riches

The vastly different results obtained from Cournot and Bertrand point to a fundamental problem with oligopoly theory:

A priori almost any outcome between monopoly and competition for the two firms combined seems plausible.

And it is possible to find assumptions that produce almost any equilibrium.

Economists have lost some of their initial enthusiasm for game theory (it dominated industrial organization in the1980s and 1990s) because it does not yield robust results.

23 Dynamic Games of Competition

24Dynamic Games

Consider decision to enter and respond to entry:

Accomodate Fight

Enter (4,5) (-1,0)

Stay Out (0,10) (0,10)

Incumbent

Entrant

Entrant gets 4, Incumbent 5

25

Dynamic Equilibria and Credible Threats for the Entry Game

• Enter-Accommodate• Stay out-Fight

There are two possible equilibrium strategies:

• The incumbent can play its “fight” strategy and brag that it will demolish the entrant.

• But what if the entrant comes in (by mistake for example)?

• Once he is in, the incumbent is better off accommodating (is there an argument that it should fight nonetheless?)

• Key principle: threat must be credible to be effective.

But one of these isn’t credible:

26Dynamic Games and Game Trees

Dynamic games are represented by game trees (“extensive form of a game”) that shows time-path of strategies:

Entrant

Incumbent

-10

45

010

EnterStay out

AccommodateFight

27Solving the Game: Backward Induction

Start with what is optimal in the “end game” and then figure out what the optimal strategy is in the previous sub-games (this is known as “backward induction”—a very powerful technique in dynamic optimization theory). 

Each player plays its best strategy in the sub-game knowing what has gone on before. This is known as the sub-game perfect Nash equilibrium.

28Nash Equilibrium for the Entry Game

Post-entry game: equilibrium is to accommodate.

Pre-entry game: given that post-entry equilibrium is to accommodate, optimal strategy is to enter.Equilibrium: Enter, Accommodate

Entrant

Incumbent

-10

45

010

EnterStay out

AccommodateFight

29Making Credible Commitments

Strategy analysis often considers whether players can make binding commitments that force them to undertake strategies that are ex post unprofitable but ex ante optimal.

For the entry game the incumbent could have “meeting competition clauses” or advertise “Our prices can’t be beat. We won’t be undersold.”

30Next week: Makeup Lecture 6.2

Part 1

Transaction Costs

Opportunistic Behavior

Theory of the Firm

Part 2

Welfare and Efficiency

Market Failures

Economics of Remedies

Antitrust, Welfare and

Market Failure