DISCUSSION PAPER

No. 15

The Impact of Compulsory Arbitration

on Bargaining Behavior

- An Experimental Study - Alexander Kritikos

December 2001

Athens Laboratory of Economic Policy StudiesDepartment of Economics

Athens University of Economics and Business

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The Impact of Compulsory Arbitrationon Bargaining Behavior- An Experimental Study -

Alexander Kritikos1

Dept. of Economics, Europa-Universität Viadrina, Frankfurt (Oder), GermanyIMOP, Athens University of Economics and Business, Greece

A series of experiments compares bargaining behavior in a Rubinstein game under three differentsettings: no arbitration, conventional and final offer arbitration. Under no arbitration disputes withzero payoffs were around 10%, while the pie was equally split in less than half of the cases. Underconventional arbitration - where the arbitrator is free in choosing his award - every third negotiationended in dispute giving incidence for a modified chilling effect. Under final offer arbitration – wherethe arbitrator has to award to the bargainers either one of their final offers - there was only a smallincrease of disputes while equal split agreements have doubled to 80%, an outcome which can bedescribed as ’destiny effect’. The experiment shows final offer arbitration, though having lowerdispute rates, to interfere more with bargaining behavior than conventional arbitration where thebargaining behavior was similar to the no-arbitration treatment. Under final offer arbitration,negotiators adjust their bargaining strategy to the arbitrator´s expected award.

JEL Code: C78, C91, D63. Keywords: Bargaining, Arbitration, Experiments, Fair Awards

Mailing address:Alexander S. KritikosFakultät für WirtschaftswissenschaftenGroße Scharrnstr. 59Europa-Universität Viadrina15230 Frankfurt (Oder)Germanykritikos@euv-frankfurt-o.de

1 This paper is part of the EU-TMR Program (No ERBFMRX-CT-960028). Support from the German ScienceFoundation under the project number Bo 747/4-2 is gratefully acknowledged. I am also grateful for the helpfulcomments of Friedel Bolle, Gary Charness, Simon Gächter, Werner Güth, Reinhard Selten and MagdalenaSwiniarska, as well as of the Seminar participants in Frankfurt, Berlin, and at the GEW workshop in Halle.Earlier versions of this paper were presented at the ESEM-conference in Lausanne, the ESA-conference in NewYork and the IAREP-conference in Belgirate/Italy.

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1. Introduction

When considering the typical structure of bargaining behavior it seems that most negotiationsare following the same ritual. Far from the efficient outcome as suggested by the RubinsteinGame [1982] where two parties sequentially bargain about the split of a shrinking pie, eachparty usually tries to claim a large part of the pie for himself. Therefore, both parties oftenlypose incompatible demands and offers. After expensive negotiations, in many casesbargaining parties tend to agree on compromises which are between the opening demands.2

The gap between theory and practice can be explained by incomplete information. Theinformation required for the Rubinstein outcome is prohibitively high: the size of the pie, thediscount rates of the bargaining parties, their 'outside options' and their subjective preferencesmust be common knowledge to secure agreements without any frictions. Negotiations becomemore complex if there is incomplete information about any of these parameters. Then, bothparties – after receiving first offers - may form expectations about each others´ preferencesand consider these expectations in their own bargaining strategies (and vice versa).3 AsKennan and Wilson [1993, p. 46] put it “from an ex ante perspective the costly process ofbargaining can be an efficient way of establishing a common information basis for anagreement“, even if it should lead ex post sometimes to a zero payoff for both parties.

Introducing the institution of an arbitrator is, therefore, suggested as a prevalent policy toreduce negotiation cost. Agreements may be settled in less amount of time so that thebargaining cost, measured by a decreasing size or a complete loss of the pie, are considerablyreduced. On the other hand, an arbitrator - if vested with the power to settle compulsoryawards – may complicate the negotiations. The bargaining parties have to consider possiblesettlements of the arbitrators in their own decision, as well.

The two most diverging schemes, conventional and final offer arbitration, and their impact onbargaining behavior are in the focus of this paper. According to Conventional CompulsoryArbitration (CCA), the arbitrator is able to impose an award of his own choice if negotiationsend in dispute, allowing him to choose freely among a continuum of potential outcomes. Itwas raised, however, that the awards might not be based on independent decisions of thearbitrators but may be affected by the bargaining process. Unyielding bargaining behavior willbecome predominant- the so called 'chilling effect', cf. Stevens [1966] - if arbitrators tend to

2 For some field evidence on costly delays, cf.Kennan and Wilson [1990a]. Moreover, Ashenfelter and Currie[1990] documented that delays in the field are not very different from those observed in experimental studies.3 The central role of information in explaining barganing behavior is discussed in the survey of Kennan andWilson [1993]. See also Roth and Murnighan (1982) for the relevance of information in bargaining experiments.

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split the difference between the final bargaining positions.4 In this case posing incompatibledemands is the best strategy: Arbitrators can be called into action in due time, and dispute costcan be kept at a low level while the higher the last claim is before asking for arbitration thehigher will be the share of the pie which the arbitrator will reward to the respective bargainer.

It was observed that dispute rates increased under CCA seemingly indicating that bargainersare discouraged to find an agreement on their own.5 Thus, conventional arbitration might siton the fence between the advantage of cost saving and the disadvantage of higher disputerates. To save the advantage and circumvent the disadvantage, Stevens [1966] proposed theother extreme among the arbitration schemes: The number of available awards is restricted totwo, i.e. the arbitrator has to choose one of the final offers of the two bargaining parties asaward, the Final Offer Arbitration (FOA).6 Dispute rates may decrease because, due to thelimited number of available awards, parties are forced to make more conducive offers thanunder CCA so that agreements may be realized without any arbitration procedure. Firstempirical papers (e.g. Stern et al. [1975]) gave evidence for decreasing dispute rates.

The incentives created by FOA were criticized for not being superior to those of CCA becausethe negotiating parties will be driven “to what the arbitrator desires. Rather than revealingtheir own preferences in the process, they reveal their perceptions of the arbitrator“ (Crawford[1979, p. 143]). Bargaining parties would not bargain in a serious way with each other.

As Crawford [1979] further showed, the theoretical implications of each design stronglydepend on the assumptions made about the arbitrators´ judgment, the information status of thebargainers (about the arbitrators) and on bargaining behavior of the two parties. In hiscomplete information model he showed that both arbitration schemes may lead to the sameoutcome if arbitrators will - irrespective of the scheme - propose the same equity orientedaward and if this will be expected by the bargaining parties.

This model poses an extreme point of view, as it excludes the possibility that arbitrators maketheir award dependent on the bargaining process – the main argument which was raised

4 For the chilling effect, see also Feuille [1975], Wheeler [1978]. Other arbitration effects which may causeunserious bargaining behavior are characterized as 'narcotic effect' (Wirtz [1963]) and as 'familiarity effect'(Farber and Katz [1979]). In contrast to the chilling effect these effects may arise only in repeated games even ifthe arbitrator has his own preferences about the awards, irrespective of the behavior of the bargaining parties.5 Field (Borchardt [1990], Currie and McConnell [1991]) as well as experimental studies (Ashenfelter et al.[1992] and Bolton [1995]) show that dispute rates increase under conventional arbitration. See also Roth [1995].6 There exist intermediate schemes, where arbitrators have more than two but less than a continuum of choices tosettle an award, such as issue by issue, tri-final offer, or multiple-final offer arbitration. See Donn [1977],Crawford [1979] and Ashenfelter et al. [1992] for description and analysis of the expected behavior under eachof these arbitration schemes. However, in this paper the focus is restricted to the two extreme points ofarbitration, final offer and conventional arbitration.

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against CCA. To hold true that the expected outcome will be the same under FOA as underCCA, arbitrators have to come in both arbitration designs to the same decision not influencedin any kind by the bargaining process. Bargaining parties have to be fully informed about thearbitrators´ expected award and have to negotiate exactly in the same way irrespective of thearbitration procedure.

There is evidence that the implications of Crawford´s analysis do not coincide with theobserved bargaining behavior: Farber and Katz [1979] showed that the outcomes under CCAand FOA are different when the parties are uncertain about the arbitrators´ preferences.Ashenfelter and Bloom [1984] found lower dispute rates and lower wage increases (in wagenegotiations in the US) under FOA than under CCA indicating that bargaining behavior seemsto be different under these two arbitration regimes. They also showed that it is difficult tospecify any further the implications for behavior of the parties if under the CCA regime thepreference function of the arbitrator contains the impasse offers of the negotiators (cf.Ashenfelter and Bloom [1984] equ. 12).

This paper aims to shed more light on the mutual effects between bargaining parties andarbitrators and on the impact of these two arbitration schemes on bargaining behavior. Wewill not only compare dispute rates under CCA and under FOA but also investigate to whichextent bargaining behavior is influenced by the incentives of each arbitration scheme. Thiswill also allow to suggest what kind of settlements the bargaining parties expect when theyask for arbitration. We further aim to find typical decision pattern of arbitrators: are theyinfluenced by the bargaining parties (cf. e.g. Borchardt [1990] Feuille [1975]) or do theydevelop independent 'appropriate' (Farber and Bazerman [1986]) or 'fair' (Crawford [1979])award criteria. Last but not least it is of central interest whether the awards are substantiallydifferent due to the restricted number of choices in FOA. Answers to these questions willallow to gather new insights which design saves most of the advantage of arbitration (the costreductions) without increasing the dispute rates and without deviating too much frombargaining behavior in negotiations without arbitration.

The rest of the paper is organized as follows. Section 2 gives an overview over relatedexperiments. Section 3 describes the three different experimental treatments, the basicRubinstein Game without arbitration as well as the conventional and the final offer arbitrationtreatments. In section 4 the main results of the experiments are reported giving an overviewover the complete bargaining process in the three treatments. In section 5 the two arbitrationschemes (and the related fairness concepts) are compared with respect to their impact onbargaining behavior and on the individual welfare of the parties. Section 6 offers a conclusionwith respect to the applicability of both aribtration designs.

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2. Results of Related Experiments

Since the basic treatment of the experimental setting is a multi-period Rubinstein game,earlier experiments with a similar design, as conducted e.g. by Neelin et al. [1988], Ochs andRoth [1989], Weg et al. [1990] and Bolton [1991], are an important benchmark. Allexperiments were Rubinstein games with three to twenty bargaining periods. In addition, Ochsand Roth [1989] varied discount factors and subgame-perfect outcomes. These studies reportthat only about half of the observed results could be explained either by the equal split7 or bythe subgame-perfect outcome, while half of the results need further explanation. All studiesalso show a small but significant share of break downs of negotiations with zero payoffs.Ochs and Roth suppose that players make strategic considerations leading for some of them toa first mover advantage (which is not always justified by subgame-perfectness). Playersfurther “try to estimate the utilities of the players they are bargaining with, and some [other]players incorporate distributional considerations in their utility functions“ (Ochs and Roth[1989]).8 They also report that the subgame-perfect equilibrium is a poor qualitative predictor.

With the exception of Ashenfelter et al. [1992] and Bolton [1995] there has been littleexperimental work on bargaining behavior under arbitration.9 Moreover, in these two papersthe arbitration procedure was not allocated to a person but was computerized, with stochasticawards drawn from a normal distribution with an expected value of an unequal split (cf.Ashenfelter et al. [1992]) and (in two differing treatments) of an equal and an unequal split ofthe pie (cf. Bolton [1995]).10 Both experiments have in common that under CCA thefrequency of disagreement increased more (due to the lower cost of disagreement) than in theno-arbitration treatment. In addition, Ashenfelter et al. observed that the dispute rates underFOA were not lower than under CCA. Bolton [1995] found out that under CCA in the equalsplit treatment usually the bargainer asked for arbitration who was closer to the equal split.

Thus, both papers showed that the institution of arbitration increases dispute rates. However,by randomizing the decision of the arbitrator they foreclosed the possibility that arbitratorswere influenced by the bargainers. Moreover, it cannot be excluded that the bargainers wereinfluenced by a computerized arbitrator in a different way than by a real-person-arbitrator. A

7 In some experiments the share of equal splits was higher than 50%.8 A more general explanation for this outcome is given by Forsythe et al. [1991] who assert that the preferencesof the participants are heterogenous.9 It has to be emphasized that there is one more experiment by Charness [2000] where the same arbitrationdesign is used as in Ashenfelter et al. [1992]. Since the experiment of Charness [2000] had a different focus thanthe present paper, these results will not be presented in this section. Nevertheless, there are remarkablesimilarities between Charness [2000] and the present experiment. These will be explained along the paper.10 Another difference in the design is that Ashenfelter et al. [1992] introduce only a time limit to the bargainersbut no discount factors and no restriction in bargaining periods while Bolton [1995] used a ‘deadline game‘.

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computerized arbitrator has the advantage that bargainers could be informed about hisprevious decisions.11 Nevertheless, it has to be pointed out that a random arbitration designwith any kind of expected value contains some disadvantages, as well. First of all, the ideathat one arbitrator can be replaced by another is not thoroughly supported by the empiricalfacts: Farber and Bazerman [1986, p. 1513] note that “arbitrators differ substantially in theirevaluation of any particular scenario in both types of arbitration. This is important evidencethat there is real uncertainty in the arbitration process due to differences among arbitrators inthe awards they made in identical situations“.

Second, the fact that there is no real arbitrator but a random draw needs to be discussed.Participants were explicitly informed (see e.g. Ashenfelter et al. [1992, p. 1412]) that theywere not able to influence the arbitrators´ decision by their bargaining behavior. Since theyprobably anticipated the random award mechanism12 it is a dominant strategy of the favoredplayers in the unequal-split treatment and of risk-seeking, risk-neutral and to a certain extenteven of the risk-averse players13 in the equal-split-treatment (at least for the specific design ofthe deadline game) to pose claims higher than the equal split. Doing so they increased theprobability of a dispute because the equal split or even more was on average guaranteed by thespecial design of arbitration. Therefore, it cannot surprise that dispute rates increased andAshenfelter et al. [1992, p. 1420] themselves concede that “part of the higher dispute rates ...is due to the asymmetry introduced by the arbitrator“.

The structure of the arbitration mechanism might also explain further findings of Ashenfelteret al. [1992]. They report that disputes were the same under FOA as under CCA. Since in theirexperiment both arbitration mechanisms relied on the same random award mechanism and thedistribution of the awards was "invariant to the arbitration scheme" [p. 1410], the arbitrationmechanism could not have a different impact on bargaining behavior in both treatments. Inparticular, the favored players had always the dominant strategy to increase the probability ofa dispute by posing higher claims, causing similar dispute rates as under CCA.14 Thus, theexperiments in these papers showed that the results under arbitration heavily depend on itsdesign. Moreover, their specific arbitration design shows that the behavior of the bargainers is

11 There are only few countries – the US among them - where in the field bargaining parties are provided withthe information of the earlier decisions of arbitrators. In most countries this is not given, mostly becausearbitrators – as elder politicians - have no award history and act as arbitrators only once or twice in their lifetime.12 A list of the last 100 decisions of the arbitrator without telling the participants the impasse offers of the twobargaining parties may even insinuate such information.13 Ashenfelter et al. [1992] argue that the data ‘not indicate ... evidence of risk aversion‘ of bargaining parties.14 A further reason for the high dispute rates under FOA in that experimental design could be the time limit offive minutes. When the bargaining parties failed to agree within that time limit, arbitration – irrespective of thedesign - was implemented automatically without being requested.

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influenced in a completely different way than under a real arbitrator. Hence, these experimentsalso reveal that negotiators react sensitive to any parameter variation in the arbitration design.

3. Experimental Design and Procedures

3.1 The Treatments

The experimental design of the present study encompassed three different treatments, onetreatment where the participants played a Basic Rubinstein game (called BR treatment)without any arbitration, one with conventional, and one with final offer arbitration. All otherconditions were kept identical. In all three treatments, two bargaining parties always had tosequentially negotiate to share a pie of DM 25,90 (13,25 Euro).

In the BR treatment without arbitration both bargaining parties had to make alternating offers.Time was divided into periods. Bargainer 1 had to divide in period 1 the pie of 259 pointsbetween the two parties. He was only allowed to make integral offers. Bargainer 2 could rejector accept. In case of rejection bargainer 2 had the chance to make a counteroffer. From thethird period on in odd-numbered periods player 1 and in even-numbered periods player 2could continue to make alternating offers. Any further proposal beyond period two induced ashrinking pie of DM 1 per period. (The pie had in the third period the size of DM 24.9, etc.).Bargaining parties had in each but the first period the choice between four options: i) to acceptthe division of the other party, ii) to make an own offer, iii) to ask the other party for anotherproposal and iv) to break off the negotiations. The experiment was designed as an ‘optionalbreak-down game‘ where both parties received a zero payment when one party chose to endthe negotiations. When both parties agreed on a division of the pie, they were paid accordingto this division. If no offer had been accepted until period 28, both parties received no payoff.

In the second treatment bargaining parties had the option to ask for arbitration (CCAtreatment). Arbitrators could fashion compulsory awards based on their own choice, e.g. onthe bargaining history or on any external judgment (e.g. a fair division). The bargaining designwas the same as in the BR treatment. It changed only with respect to choice iv): the partieshad the option to ask for conventional arbitration if the negotiations ended in disagreement.The bargaining cost per period was fixed – as in the BR treatment - at 1 DM per period. Thethird treatment was designed as final-offer arbitration (FOA treatment), again withcompulsory awards. When negotiations ended in dispute (choice iv) bargaining parties hadagain the option to ask for arbitration. However, arbitrators selected now one of both parties´final offer as settlement. Bargaining cost were fixed again at DM 1.

3.2 Procedures

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ORGANIZATION: In the entire experiment 300 undergraduate students from all faculties of theEurope-University participated in the three treatments as bargainers and 20 graduate studentsas arbitrators. Bargaining participants were recruited by verbal and written announcements.Their participation required appearance at a prearranged place and time, and was restricted toone session. Upon arrival, participants were randomly assigned to their roles as bargainer 1 or2. 100 students were assigned to each treatment where two participants had to bargain witheach other. Throughout the sessions participants were placed in two separate classrooms. Allexperiments were conducted once, after the participants had received written and verbalinstructions about the setting, the four possible choices in every period and about thearbitration modus (see Appendix B). All participants were anonymously and randomlymatched. Each participant had practiced one test-run where they played a complete game.15

PROCEDURE: The negotiations were played sequentially. Together with the instructionsbargainer 1 received in period 1 the bargaining record shown in Appendix A. Having made aproposal, the sheet was transferred to the assigned bargainer 2. He was expected to make oneof the four choices mentioned above. The sheet was taken back and forth until an agreementor a disagreement (and in the arbitration treatments a compulsory award if requested) wassettled. Participants were immediately informed about their payoffs. Throughout the sessionsnobody was informed about the identity of his partner. Participants received their payoffsfrom a third party not involved in the experiment. Participants were required to reveal theirpassword to the third party in order to get paid. These features ensured the one-shot nature ofthe experiments. Sessions lasted between 45 minutes and one hour. The average payoff wasmore than DM 10 which covered the opportunity cost of participation.

INFORMATION: Participants had complete information about the size of the pie, the bargainingcost and the arbitration mechanism, thus, the game was designed to be one of commonknowledge about the "objective" payoffs.16 Moreover, they knew that the bargaining record (iftheir negotiations ended in dispute) would be anonymously passed to the appointed arbitrator.Participants were informed about the rules of conventional and final offer arbitration.

ARBITRATORS: For each arbitration treatment 10 arbitrators were independently recruitedfrom the graduate programs of the same university. Whenever negotiations ended in a disputethey received anonymous bargaining records. Without being able to communicate with thebargaining parties they were required to settle their own award in case of CCA or to chooseone of the two final offers of the parties in case of FOA. Besides the bargaining protocol and 15 The experiments were not repeated because this paper was not focused on learning curves. In order to makethe participants sufficiently familiar with the experimental design, the test-run was introduced.16 At the same time it should be emphasized that players had – of course – incomplete information about thepreferences of their bargaining partners.

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the size of the pie no information was given to them. They were not able to favor anyparticular participant. Arbitrators were paid DM 5 per award regardless of their decision.

3.3 Hypotheses

In the present paper the game theoretic outcome is used as hypothesis for the BR treatment. Itcan be computed by backward induction. The subgame-perfect equilibrium would be thatbargainer 1 in his opening offer divides the pie DM 12,9 : DM 13,0 in favor of bargainer 2and that bargainer 2 accepts that split. Although rejected in several experiments, it will berelied on this hypothesis because it is not only the subgame perfect but also a fair outcome.

As we saw above, the outcomes under the two arbitration procedures strongly depend on thepreference function of the arbitrators and the expectations of the bargaining parties. For theconventional arbitration design, we may use the chilling effect as a benchmark for thehypothesis. Arbitrators are expected to make awards dependent only on the impasse offers ofthe two bargaining parties. In that case the two bargaining parties instead of revealing theirown preferences are expected to claim infinite amounts or at least the complete pie forthemselves. Parties, further, would make no concessions and would ask for arbitration after asmall number of or one bargaining period. This would lead to high (or from a normative pointof view to a 100%) dispute rate(s). The probable award would be the equal split of the pie.

With respect to the final offer arbitration, we may use as benchmark the approach of Crawford[1979]. Players then would expect that arbitrators make awards using independent criteriawhere in the present experiment the most reasonable award is the equal split and if none of thefinal offers is the equal split, the award would be the final offer which is closer to the equalsplit. Bargaining parties, however, in order to avoid an award favoring the other player wouldthen agree on the equal split without arbitration procedure.

4. Results

This section starts with the presentation of dispute rates in the different treatments. Following,typical patterns of bargaining behavior explaining the dispute rates and other results of eachtreatment will be ascertained. As already noted, the BR treatment serves the purpose of beinga baseline for comparison with the arbitration treatments and may provide insights into howdifferent designs of arbitration may influence the bargaining behavior.

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It has to be emphasized that in the second and fourth column of table 2 as well as in Figures1a, b and 2 the final claims are displayed as if the pie has always the hypothetical size of DM25,90, i.e. it is not shrinking.17 This is done in order to enable a comparison of all final claims.

4.1 Dispute Rates

Table 1 displays the dispute rates for each treatment. In the BR treatment 8% of thenegotiations ended in disagreement – players received no payment at all. As expected fromprevious studies the dispute rates were increased by the introduction of conventionalarbitration from 8% in the BR treatment to 34% in the CCA treatment.18 (Fisher´s test showthese differences to be significant, with p= 0.001, see Siegel and Castellan [1988]).19

- insert Table 1 about here -

In contrast to this the FOA treatment shows that the final offer arbitration - where 14% of thenegotiations ended in disagreement - does not significantly increase the dispute rates ifcompared to the BR treatment (Fisher´s test shows p=0.26)20 while a comparison of the FOAwith the CCA treatment shows a significant decrease in disputes (p=0.017).

Result 1: Under BR 8% of the negotiations end in dispute with a zero payoff. The loss of thepie can be prevented by arbitration. However, the existence of conventional arbitratorsincreases dispute rates. In contrast to this under FOA dispute rates are as low as under BR.

4.2 Disagreements and Awards

The question which party asked for arbitration allows to gather first insights into theexpectations of the bargaining parties. To differentiate the bargainers, the party whose firstclaim (for itself) in periods 1 and 2 was above the median will be called 'the far bargainer', theparty whose first claim was lower than the median will be called 'the close bargainer'.

17 Thus, when e.g. the bargaining parties negotiated for four periods the pie as calculated in Table 2 had still thesize of DM 25.9 instead of DM 23.9. An offer of bargaining party 1 in period 4 of DM 20.0 for itself and of DM3.9 for party 2 (thus, with a pie size of DM 23.9) was transferred into a claim of DM 21.0 for bargaining party 1and an offer of DM 4.9 for party 2. The advantage of doing so is that we can more easily reveal to which extentbargaining parties were in later periods ready to offer an equal split.18 This compares to 11.2% in the Ashenfelter et al. [1992] treatment with no arbitration and 33.8% under asimilar CCA. Moreover, these results show a certain consistency with the field experience: Ashenfelter andBloom [1984] found that about every third wage-negotiation is solved by arbitration.19 Besides, the cost of arbitration might also have an influence on the rate of disagreement, see Bloom [1981].However, this factor was not varied in the present study.20 This result is in contrast to Ashenfelter et al. [1992]. The reason is certainly the different design of FOA.

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In the CCA treatment 17 negotiations ended in dispute. In 12 cases a far was matched with aclose bargainer where in 9 cases the far and in 3 cases the close bargainer called forarbitration.21 Thus, bargainers may have expected arbitrators rather to decide in the favor ofthe far bargainer. This expectation received support to be correct. In 11 cases the arbitratorssuggested an unequal split (Figure 1a), similar to difference-splitting and, thus, in favor of thefar bargainer. There was one award which allocated the equal split to both bargainers (wherethe far bargainer had asked for arbitration). Far bargainers when matched with closebargainers could generally expect to be awarded with a 'split the difference' decision and,hence, with more than 50% of the pie.22 Figure 1b shows that in the other 5 cases two farbargainers were matched.23 Moreover, in the 5 cases the bargainers (by having the samedistance to the equal split) signaled to the arbitrator to be interested in an equal split, but didnot manage to agree on it. The arbitrator awarded the equal split.

- insert Table 2 and Figures 1a, b and 2 about here -

In the FOA treatment 7 disputes were observed, all machings of far with close bargainer (seeFigure 2). Here, in 5 cases it was the close and in 2 cases it was the far bargainer who askedfor an external award indicating that under FOA the close bargainer expected to be favored bythe arbitrator. Again, these expectations coincided with the decision of the arbitrator. In twocases the arbitrator had the choice between an equal and an unequal split (the two final offers)and preferred the equal split. In five cases the arbitrator had to choose between two unequalsplits. In all five cases the less unequal split of the close bargainer was awarded in his favor.

Result 2: (1) Under CCA, far bargainers more often than close bargainers ask for arbitration.Awards correspond to the split the difference notion and are in favor of the far bargainer, if heis matched with a close bargainer. When two far bargainers are matched the award resemblesto the equal split. (2) Under FOA, close bargainers ask more often for an award. Arbitratorsalways prefer the less unequal split, i.e. they decide in favor of the close bargainer.

4.3 Opening Offers

In order to reveal the path leading to the diverging dispute rates and to the expectations aboutthe awards it is necessary to analyze opening and final offers. Starting with the opening offer,Table 1 compares the average first claims in all treatments. The average first claim in the BRtreatment was around DM 18.0, as Table 3 shows in about 80% of the cases far from the 21 This is in contrast to Bolton [1995] where mostly the close bargainer induced arbitration. The reason for thedifferent behavior is – as we will see – once more the differing incentive of each arbitration design.22 The average award allocated to the 11 far bargainers was DM 15.11 (minus the negotiation cost per period).23 These 5 cases also differ from the mentioned 12 negotiations as they took more than four bargaining periods.

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subgame-perfect opening offer.24 Bargaining parties were testing their partner´s willingness ofrejecting unequal splits. This strategy was not only successful in the sense that 6 bargainersrealized a kind of first mover advantage where bargainers 2 did agree to the unequal split,25

but also in the sense that bargainers, when confronted with a counter-offer, tried to find outthe type they were matched with. This kind of bargaining strategy corresponds to the approachof Kennan and Wilson [1993] where the level of the opening demand is one way ofexchanging signals between the bargaining parties.

- insert Table 3 about here -

In the CCA treatment the average opening offer significantly increased to DM 19.2 comparedto the average opening offer in the BR treatment. (The Kolmogorov-Smirnov test revealsD=0.268 leading to χ2 = 7.18, for df=2 is p=0.03). In contrast to this, the average first claim inthe FOA treatment was almost the same as in the BR treatment.

By comparing the average first claim ending in dispute with the average first claim leading toan agreement (without having sorted into far or close bargainer) it is possible to further revealthe influence of the arbitration design on bargaining behavior (Table 2). The average firstclaim in the CCA treatment leading in later periods to disagreement was with DM 22.37 ashigh as in the BR treatment (DM 22.0). The same holds for observations leading to anagreement: the average first claim was DM 17.57 in the CCA and 17.64 in the BR treatment.Differences between first claims leading to an agreement and those leading to a dispute arehighly significant under CCA. (The Mann Whitney U test shows for CCA U=304, p<0.0003).

Thus, there was a similar spread in the first claims of the BR and the CCA treatment. Thismeans that the difference in behavior between BR and CCA is not that all participants posedhigher claims but that some persons switched from the typical first claim leading to anagreement to the typical first claim which also contained the risk to end in disagreement (seealso Table 3 where the first claims are clustered into eight groups).

There is another striking result. The chilling effect expects negotiators under conventionalarbitration not to reveal their true preferences. Consequently this would mean that they maydemand infinitely high claims or at least the complete pie in order to influence the arbitrator intheir direction. In the CCA treatment there was only one participant who demanded the wholepie of DM 25.9 for himself. He was awarded with slightly less than half the pie (see Figure

24 Similar results are found in many other experiments, see e.g. Ochs and Roth [1989], Bolton [1991] and in theoverview of Roth [1995] where it is also emphasized that the subgame-perfect outcome is a poor point predictor.The reason for the particularly low share of subgame-perfect offers in the present experiment might be that thenegotiation cost per period, i.e. the cost of exchanging signals were (with DM 1) relatively low.25 A similar behavior was observed by Bolton [1991].

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1a). Thus, on the one hand, some bargaining parties expected to be able to influence thearbitrators. On the other hand, it seems as if the bargainers conceived that there might be alimit of credible demands up to which an arbitrator can be influenced towards their preferredoutcome. Beyond that limit arbitrators may introduce their own external jugdment.

Considering the FOA treatment, Table 3 reveals differences in the distributional structure offirst claims between the FOA and the BR treatment. While in the BR treatment the first claimsare divided into two segments - about 50% of the participants claimed for themselves amountsbetween DM 13 and DM 16.5 and about 40% amounts between DM 20 and DM 25, in theFOA treatment almost 80% of the participants posed first claims less than DM 20.26

Thus, the first claim in the FOA treatment was (with almost DM 18) on average the sameregardless whether negotiations were concluded by arbitration or by agreement. The fact thatthe close bargainer may ask straightforward for arbitration possibly resulting for the farbargainer in a payoff of less instead of more than 50% of the pie, induced parties who mighthave posed high first claims in the BR treatment to be more cautious in their first claims underFOA. A considerable number of players was afraid of provoking an early break-off of thenegotiations so that only about 20% of the first claims were higher than DM 20.

Result 3: (1) The first claims in the CCA treatment and in the BR treatment show the samespread where participants in negotiations ending in disagreement systematically pose higherclaims then in negotiations ending in agreement. There are more participants in the first periodof the CCA treatments than in the BR treatment demanding the ‘disagreement claim‘. (2)Participants may have expected that there is a barrier of credible first demands – only oneparty demands the complete pie. (3) The first claims in the FOA treatment are not higher thanin the BR treatment but different in their distribution structure.

4.4 Final Offers

Table 2 displays the average final claims (the claim is displayed as if the pie does not shrink).Again, results are disaggregated with respect to the fact whether negotiations ended in agree-or disagreement. In case of an agreement Table 2 shows the average amount which the farbargainer received in case of an unequal split. In case of a dispute it shows the averageimpasse offer of the far bargainer and his average payoff in case of an unequal award.

26 In order to test this hypothesis, the first demands were clustered into three groups (group 1 contained claimsbetween DM 10 and DM 14, group 2 between DM 14 and DM 20 and group 3 between DM 20 and DM 25). Aχ2-test comparing the subgroups of the BR treatment with the FOA treatment reveals that the hypothesis that theshare of first claims was for the BR and the FOA treatment the same in the three subgroups can be rejected atp<0.05; χ2 = 6.9, df=2.

15

The first important result is that in the BR treatment only 38% of all negotiations (41% of thesuccessfully finished negotiations) resulted in an equal split.27 Thus, more than half of allnegotiations were concluded with an unequal split although the equal split was not only thefair but also the subgame-perfect outcome. The average payoff of the 27 far bargainers wasDM 15.22 (when using the full size of the pie). No far bargainer received less than 50% of thepie.

In contrast to this, in the arbitration treatments most negotiations resulted in an equal split ifthe parties succeeded to find an agreement. This result is supported by column 4 which showsthe number of equal splits, i.e. 27 of 33 (82%) in the CCA and 39 of 43 (90%) in the FOAtreatment (related to the negotiations ending in a voluntary settlement). The payoff of the farbargainer was significantly lower in both arbitration treatments than in the BR one (p<0.001).

The differing impact of the two arbitration methods, however, becomes particularly clearwhen we relate the shares of equal splits to the total observations in each treatment. In theconventional arbitration treatment only some more participants (54%) accepted an equal split(which is already significantly higher than in the BR treatment, p=0.04). In contrast to this, theshare of equal splits mounts to 78% in the FOA treatment, significantly more than in any othertreatment (the Fisher test reveals p=0.01 when comparing the FOA with the CCA treatment).

Another striking difference appears when the average final offers are compared with theaverage first offers. In the BR and the CCA treatment participants were ready to make similarconcessions towards their bargaining partners as the number of periods increased. The samebehavior was observed in the FOA treatment when the negotiators made an agreement. Inthose cases ending in dispute under FOA, far bargainers made less concessions. It seems thatthose bargainers aiming to realize an unequal split tried to cope with the impact of final offerarbitration as much as possible. In the first period - as already mentioned – they were verycautious and did not ask for higher shares of the pie than other bargainers, holding on thedemanded share in the subsequent periods. This could be interpreted as a strategy to convincethe close bargainer to accept an unequal split. However, the expectations of this minority offar bargainers failed when they were too far from the equal split.28 They went into arbitrationand were not favored by the arbitrator who preferred the less unequal split.

27 Similar low shares of equal splits were found in a five period Rubinstein game by Neelin et al. [1988] and inthe unstructured time limited bargaining game by Ashenfelter et al. [1992].28 As we saw before, some negotiations ended in an unequal spit to which both parties deliberately agreed towithout FOA. In contrast to the behavior decribed above, in these cases the far bargainer made higherconcessions. The difference to the equal split which the far bargainer could realize was on average DM 1.

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Result 4: (1) Compared to the BR treatment, in the FOA treatment more than in the CCAtreatment the existence of an arbitrator induces far bargainers to voluntarily agree on an equalsplit. (2) In the BR and in the CCA treatment bargainers make similar concessions. In contrastto this in the FOA treatment, if negotiations end in dispute, far bargainer tend to make lessconcessions during the negotiations.

4.5 Bargaining Periods and Payoffs

Another important factor is whether the design of arbitration has any impact on the number ofbargaining periods, hence on the efficiency of each design. Earlier discussion would suggestthat negotiations under the safety net of arbitration would lead in the extreme case to only onebargaining period. Table 2 shows for all treatments the average number of bargaining periodsin case of a settlement and in case of a dispute. When comparing the number of periods withnegotiations ending in an agreement and those ending in dispute it becomes apparent that inall treatments the average number of bargaining periods was shorter when the parties came toan agreement. This might mean that even in the arbitration treatments the participants didsome additional efforts to come to an agreement without arbitration before asking for anexternal award. The comparison of the FOA with the CCA treatment (Table 5) shows thatparticipants were even more patient or cautious under the FOA treatment and preferredanother period of bargaining before they submitted to the arbitrator.29

- insert Tables 4 and 5 about here -

Before discussing the outcomes under the three treatments in the next section, it is worth tocompare the payoffs, the parties could realize in each treatment. Table 4 displays the averagesize of the total pie.30 Due to the differing numbers of bargaining periods and due to the factthat in the BR treatment four negotiations ended in dispute (with a zero payoff) the threesettings have relatively different properties which are summarized in the following welfareranking. As a benchmark we include the outcome under the Rubinstein solution (Rub).Starting with the total size of the pie (P), we get the following ranking:

PRub > PCCA > PFOA > PBR

29 A statistical comparison showed that in the BR and the CCA treatment parties negotiated over a similarnumber of bargaining periods (see Table 5). In contrast to this result, comparison of the CCA and the FOAtreatment showed a lower number of bargaining periods in CCA (p=0.067).30 This means for the BR treatment that the cost per bargaining period and the share of zero payoffs (if negotia-tions ended in dispute) were deducted from the full size of the pie (DM 25.9). In the other treatments bargainingcost arising after the second period, were substracted from the pie. In all arbitration treatment the payoffs of thosefar and close bargainers whose negotiations ended in disagreement, were calculated according to the award.

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Thus, it is true for all kinds of arbitration that the existence of an arbitrator increases theoverall welfare.31 The average size of the pie was larger in both arbitration treatments than inthe BR treatment, in particular because the bargainers were able to avoid zero payoffs whentheir negotiations ended in dispute. However, as we saw before there were no cost savings dueto a smaller number of bargaining periods.

Focusing on the average payoffs of far and close bargainer, the ranking is:

farRub ≅ closeRub ≅ farCCA > farBR > farFOA ≅ closeFOA > closeCCA > closeBR

In order to compare the quantitative differences between the treatments the average payoffsare displayed in Table 4. It is worth emphasizing that, when comparing the CCA treatmentwith the BR treatment, the average payoff increased by 3.5% for the far and by 11% for theclose bargainer. The same comparison of payoffs in the FOA with the BR treatment showsunder FOA a 3% payoff decrease for the far and an 15% increase for the close bargainer.

Both results are surprising. Under CCA, there was consent that close bargainers may behandicaped by an arbitration scheme where the splitting of the pie is in favor of farbargainers.32 Results in Table 4 show that rather the opposite was found: it was the closebargainer who gained more from the institution of arbitration, although awards according tothe split the difference notion in the CCA treatments were observed. In the FOA treatment,there were 41 equal splits, 4 agreements in favor of the far and 5 awards in favor of the closebargainer. Close and far bargainer received on average the same share of the pie.33 Theremarkable result of the FOA treatment is that the far bargainer gained on average less than inthe BR treatment, although in the FOA treatment no disagreements with zero payoffs arose.

Result 5: (1) Negotiations ending in dispute were proceeded over a higher number ofbargaining periods, irrespective whether or not arbitration was available. (2) The average sizeof the pie is largest in the CCA treatments. (3) An increasing share of equal splits in thearbitration treatments increases the payoffs of the close bargainers.

4.6 Other Observed Regularities

The results allow to describe some regularities of bargaining behavior. Previous studiesasserted bargainers to have heterogenous preferences being not only related to the subgame

31 See Currie and McConnell [1991] who also showed for the field data that compulsory arbitration pareto-dominates no arbitration.32 See e.g. Borchardt [1990].33 The average payoff is different after the second digit after the komma.

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perfect outcome.34 Differing preferences were also expressed during the complete process ofthe present experiment, starting with the first offers. Therefore, according to the distributionof opening offers in the BR treatment, we may roughly categorize the parties into two types:weak and firm bargainers35 who eventually became close and far bargainers. The spread ofopening claims in the BR treatment (see Table 3) allow the further assumption that weak andfirm bargainers are equally distributed in the population with 50% each,36 and that due to therandom matching in about 50% of the cases a weak was paired with a firm bargainer andweak and firm bargainers were paired with each other in about 25% of the cases.

In order to be able to interpret the data it should be further assumed that some bargainers areless risk averse than others. More specifically, with respect to risk aversion it is assumed thatthere are again two types of bargainers. Participants with lower risk-aversion may bargain in away that the probability of a break down of negotiations is higher – with either zero payoffs inthe BR treatment or an unknown award in the CCA treatment.37

Applying these two assumptions to the results leads to the following explanation: When in theBR treatment firm bargainers were matched with weak bargainers, the latter ones were mostlywilling to accept an unequal split of the pie. This explains the 27 observations with an unequalsplit.38 All matches of weak with weak bargainer and most of the matches of firm with firmbargainer lead to an equal split explaining 19 observations. Four cases ended in a break downwhere in three cases a firm was matched with a weak bargainer, and in one case two firmbargainers were matched with each other.

In the CCA treatment there was a similar spread in the opening claims as in the BR treatmentwhere we also observed a similar share of firm and weak bargainers (about 50% each) and asimilar matching. However, in the CCA treatment there were more negotiations resulting in anequal split. The data give certain incidence that a similar share of matches as in the BRtreatment where the same bargaining types were negotiating with each other, ended again inan equal-split-agreement. The increase of equal splits can be interpreted in the line of the 34 Earlier research found that there is not only an equilibrium-dependent but also type-dependent bargainingbehavior. See Malouf and Roth [1981] and Ochs and Roth [1989] and, more recently, Charness [2000].35 Other possible labels for their differing behavior could have been fair (instead of weak) and egoistic (insteadof firm). Since firm and weak are more neutral terms these two labels are used throughout the paper.36 A similar distinction was done by Charness [2000] who explicitly separated two types by their willingness tospend differing amounts of money in the Dictator Game. It is remarkable that in his experiment also about 50%of the participants received the lable ‘low type’ (which corresponds in the present study to the firm bargainer)and about 50% were ‘high types’ (here weak bargainers).37 As we will see the second assumption does only apply for the BR and the CCA treatment. For the FOAtreatment the expectations about the arbitrator award were clearly such that even firm bargainers with low riskaversion aimed to avoid arbitration.38 Interestingly, in treatment 2 of Charness [2000] which is similar to the present study firm bargainers whenmatched with weak bargainers were also able to secure a significantly higher share of the pie for themselves.

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second assumption: some firm bargainers when matched with a weak bargainer were notsufficiently sure in their expectation whether the arbitrator will make an award according todifference-splitting. These firm bargainers preferred an equal split with a weak bargainer to anunknown outcome under arbitration.

In the other matches of firm with weak bargainers in the CCA treatment, the negotiationsresulted again in unequal splits. In 10% of all cases the firm bargainer realized an unequalsplit without arbitration, now with an average payoff of DM 13.6 - a lower level than in theBR treatment. In about 25% of the CCA observations the bargaining between firm and weakbargainer ended in arbitration, almost always with an award which allocated a higher share ofthe pie to the firm bargainer.

In the FOA treatment, bargaining behavior was different. While it is possible to distinguishbetween far and close bargainers, there is no clear spread in the first claims as in the othertreatments because – as shown in section 4.3 – far bargainers decreased their first claims.Nevertheless, we may assume that there is a similar share of firm and weak bargainers as inthe BR treatment. Assuming further that there were the same shares of same and different typematchings it is possible to assert that 50% of the outcomes resulting in equal splits mayaccount for matches of same types. However, in order to explain the remaining 30% of equalsplits it seems that many firm bargainers tried to avoid a dispute when matched with weakbargainers. The chance of getting less than 50% of the pie if the arbitrator would choose thesmaller unequal offer disciplined the firm bargainers. It led them often to accept or proposeequal splits. Only 11 far bargainers, probably matched with close bargainers, tried to realizean unequal split of the pie even under the risk of running into arbitration. 4 of them weresuccessful in this strategy and realized a slightly unequal split. The other 7, demanding a moreunequal split, went into arbitration. In two cases the close bargainer proposed an equal split inhis final offer (which was then chosen as award). The other 5 far bargainers were matchedwith a more sophisticated close bargainer who had proposed a less unequal share of the piethan the far bargainer. In all cases the arbitrator preferred the less unequal split as award sothat these far bargainers left negotiations with less than 50% of the pie.

5. The Impacts of Compulsory Arbitration

The previous section showed that the total welfare for both bargainers was higher under CCAthan under FOA and than in the BR treatment. This section will discuss the impact of thedifferent arbitration schemes on bargaining process and on the individual welfare. These twovariables might be the central variables when it is aimed to evaluate the impact of differentarbitration schemes on the outcome of a bargaining game.

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With respect to the first variable we focus on the bargaining process which is different in thetwo arbitration procedures. Therefore it will be analyzed which mechanism interferes to alesser extent with bargaining behavior. For this reason bargaining patterns under botharbitration schemes are compared with the typical bargaining behavior in the BR treatment.

How can we describe the interdependencies between bargainers and arbitrator underconventional arbitration? On the arbitrator’s side it seems that their preference functioncontains more arguments than the impasse offers of the negotiators: Arbitrators evaluated theinformation they could gather from the negotiation process. Having received correspondingsignals, arbitrators awarded the equal split, when the same type was matched, and mostlymade awards relative to the demanded shares, when two different types were matched. Thus,arbitrators were willing to make decisions according to difference-splitting, at least ifnegotiators gave them the impression of serious bargaining.39 On the other side, even if therewas only one firm bargainer with a non-compromising bargaining strategy, the award was notdepending on his impasse offer anymore but was based on an external judgment.40 We maytherefore reinterpret the arbitrator´s behavior: Arbitrators are not unilaterally influenced by thebargaining behavior. They rather weight different possible awards against each other and needto be convinced by the strategy of the bargainers in order to engage in difference-splitting.

To which extent did bargaining behavior change under conventional arbitration? Havingseparated between the two bargainer types many similarities can be found when comparingthe CCA with the BR treatment. In contrast to the hypothesis (see section 3.3), first offers hadthe same distribution structure. Firm bargainers were ready to make similar concessionsduring the bargaining process and bargained over a similar number of bargaining periods.Matches of weak with weak and firm with firm bargainers resulted in equal splits in bothtreatments. Differences between the two treatments were found insofar, as about half of thefirm bargainers (and not all bargainers as suggested by the chilling effect) increased their firstclaims and as the weak bargainers (if mixed with one of these firm bargainers) made lessconcessions than in the BR treatment before they went into arbitration.

Therefore, it is necessary to focus on the type of award if participants asked for arbitration.The introduction of the arbitrator was partly a welfare enhancing decision since somenegotiations had ended in a break-down with zero payoffs in the no-arbitration treatment. In

39 As mentioned in the introduction, a similar (not any further specified) preference function for the arbitratorwas proposed by Ashenfelter and Bloom [1984] in equation 12. The outcome of the present experiment mayopen the line for future research about further specification of this equation.40 First experiments where arbitrators were confronted with hypothetical bargaining protocolls support theassertion that the awards correspond only to difference-splitting if arbitrators had the impression of a seriousbargaining strategy. Such a strategy implied that bargainers although asking for a high share do not simplydemand the complete pie and do make concessions towards their partners. For further details, cf. Kritikos [2001].

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case of a firm - firm matching, these negotiations resulted under conventional arbitration in asettlement where half the pie was awarded to each party. The award was similar to theoutcome in the BR treatment when two firm bargainers succeeded to make an agreement.

If a firm with weak matching resulted under CCA in disagreement arbitrators mostly engagedin difference-splitting. While this outcome should favor the relatively stronger bargainer, thepayoff analysis in section 4.5 showed that the difference between the two average pie sizes (inthe BR and the CCA treatment) was mostly gained by the weak bargainer.

There are two effects which explain this seemingly paradoxical outcome. The first effect isthat conventional arbitration disciplined some among the firm bargainers. They preferred arelatively lower share of the pie to the risk of an uncertain award and agreed to an equal splitor induced a split less unequal than under the BR treatment. The second effect concerns thearbitrator awards per se: A comparison of the average CCA arbitrated payoff of the firmbargainer (when matched with a weak bargainer and when awards were according to the split-the-difference notion) with the average payoff in the same type of matching under the BRtreatment, shows in both treatments a similar unequal share of slightly more than DM 15 infavor of the firm bargainer. Thus, firm bargainers did gain the same amount in the CCAtreatment as in the BR treatment if they asked for arbitration and gained less if they found anagreement without arbitration.

It has to be emphasized in this context that the strategy of the firm bargainer has to bedifferent in the CCA treatment in order to receive under difference-splitting the same share ofthe pie as in the BR treatment. Since weak bargainers under conventional arbitration seemedto be less willing to accept unequal splits, firm bargainers might have anticipated the necessityof asking for arbitration. When they expected that awards will be done according todifference-splitting, they needed to claim a higher share then under BR. Assuming that thefinal offer of the weak bargainer was the equal split, that the concessions of the far bargainerper negotiation period were the same as in the BR treatment, the firm bargainer has to increasethe first offer in a way that the difference between his impasse offer and the impasse offer ofthe weak bargainer is at least the double of the difference between the realized payoff of thefirm bargainers in the no-arbitration treatment and the equal split.

With respect to the mutual impact of conventional arbitration on bargainers and arbitrators wemay conclude: a high share of negotiations – even those where arbitrators made splitting-the-difference settlements - ended under conventional arbitration in a similar type of pie-splittingas without arbitration. The observed effects can be captured in the following

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Conclusion 1: (1) Negotiations which might have ended in dispute without arbitration aresettled by award under CCA increasing the payoff of all types of bargainers. (2) About half ofthose firm bargainers who might have realized an unequal split in the no-arbitration treatmentwhen matched with weak bargainers were more cautious than in the BR treatment. UnderCCA, they preferred the equal split or a less unequal split to a risky arbitration procedure. Thissecond effect is in favor of the weak bargainer. (3) 50% of the firm bargainers who werematched with weak bargainers realized the same unequal split in the CCA treatment (byasking for arbitration) as in the BR treatment. (4) There is a modified chilling effect: Firmbargainers have to increase their first offers in order to secure the same share of the pie viaarbitration as they might have secured in the no-arbitration treatment.

Thus, the central obstacle raised against conventional arbitration – higher dispute rates than inthe no arbitration treatment - is discovered to be a purely strategic effect.

Turning to the final offer arbitration, it is argued that due to its lower dispute rates it should bepreferred to conventional arbitration. The key to reveal the main reason for the lower disputerates is the restricted number of possible awards. For the arbitrator this restriction foreclosesthe possibility to consider the exchange of signals between the two parties in the same way asunder conventional arbitration. Consequently, while conventional arbitrators showed to havepreferences with two variables - external judgment and individual bargaining behavior - thepreferences of final offer arbitrators seem to be reduced to the variable ‘external judgment‘with the following scaling: a preference for the equal split if one final offer was the equalsplit, if none of the bargaining parties offered an equal split, a preference for the less unequalsplit. Arbitrators were not able to mediate between the bargaining parties as under CCA.41

Restricting the awards in that manner has a strong impact on bargaining behavior if partiesanticipate the consequences of such a restriction - as most of them probably did. Starting withthe arbitrator, his specific preference system turns the splitting upside down, because heprefers the less unequal claim yielding more than half of the pie to the close bargainer. Thisaward system forces firm bargainers to be cautious: Instead of revealing their own preferencesthey made to a lesser extent first offers far from the equal split. Those parties who claimed ahigh share in the first period made more concessions in subsequent periods, willing to acceptequal splits of the pie in order to avoid arbitration. A minority of bargainers revealed theirpreferences during the negotiations. They made less concessions with increasing bargainingperiods to induce their counterparts to agree on an unequal split. This strategy failed when

41 It remains open whether they refused to use the more unequal split as award because they were not convincedby the strategy of the far bargainer or because they had a singular preference for the less unequal split of the pie.

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their bargaining counterpart asked for arbitration and where payments were allocatedaccording to the rule claimed above. This leads to Conclusions 2 and 3.

Conclusion 2: Under FOA almost all games ended in an equal split or not far from the equalsplit. There is a destiny effect: In order to avoid disadvantageous awards, participants did whatthey expected the final offer arbitrator would do.

Thus, the low dispute rate is realized because most negotiators probably revealed theirperceptions of the arbitrator preferences. The present experiment allows

Conclusion 3: (1) Due to the different number of available choices the arbitrators were forcedto make substantially different awards in FOA and CCA, inducing differing behavior of thebargaining parties. (2) Bargaining behavior is more interfered under final offer arbitration.

Turning to the consequences of both arbitration treatments for the individual welfare, it comesto the question of a fair award – either the equal split or a flexible award according todifference-splitting. Thus, there are two fairness concepts: Decisions according to an externaljugdment or decisions relative to the bargaining types in addition to an external judgment.

It seems to be common sense that the fair division of a pie is the equal split (see e.g. Rawls[1971]). This may also guide the judgment of a fair award when asked for arbitration – beingagain the equal split. In favor of this solution Rawls further argues that unequal splits are onlyjustified if both parties are better of than under the equal split. Therefore, according to thiscriterion the Final Offer Arbitration should be preferred to the Conventional Arbitration.

If applying the Pareto-criterion the conclusion would be different. First of all, it is criticalwhich payoff is used as benchmark in comparison with the outcomes under CCA and FOA. Incomparison to the Rubinstein solution the close bargainer seems to be worse off under CCA.Since the normative approach of the Rubinstein game forecloses the possibility of havingdifferent types of bargainers, it would be the correct benchmark only if these types had beencreated by the introduction of arbitration and if in the BR treatment bargainers had behavedsimilar to the normative predictions of the Rubinstein approach. However, the BR treatment –as many other experiments - showed the opposite. Firm and weak bargainers exist in the BRtreatment in a similar distribution as in the CCA treatment. Hence, it is more reasonable tocompare the outcomes under arbitration with those of the BR treatment.

The introduction of the Pareto criterion means that both parties would be asked what kind ofarbitration they would support according to their payoffs under the BR treatment. This

24

criterion shows that on average both bargaining types would support conventional arbitrationbecause they are able to improve their payoff in comparison to the no arbitration treatment.

Asked for the consent on FOA we may observe a conflict. FOA signifies no Paretoimprovement for the average far bargainer in comparison to the no arbitration treatment.Players who may had behaved as firm bargainers in the BR treatment, would reject FOA. Ifasked to choose between the two arbitration schemes, they will rather prefer this arbitrationscheme whose award structure reflects the relative strength of each bargaining type.42

Conclusion 4: Asking for the consent of both bargaining types, only bargainers who behavedas weak types in the BR treatment would support both arbitration schemes. Bargainers whobehaved as firm types would support conventional and reject final offer arbitration.

6. Conclusion

The present experiment gives incidence that the bargaining outcome in a Rubinstein Gamestrongly depends on the design of the arbitration mechanism. Asking the hypothetical questionwhich arbitration design should be installed, the choice depends on the the purpose of theinstitution to decide. If the aim is to guarantee completely uninterfered negotiations, noarbitration should be introduced. Free negotiations implicate that parties have to make signalsin order to give credible information about their preferences even if that costly process ischarged as inefficient from an ex post perspective, even if there are many bargainingoutcomes far from the equal split and even if bargainers may choose to break off negotiationswith zero payoffs.43 This means in other words to accept the fact that there are types ofbargainers who have heterogenous preferences which may lead in a bargaining environment toseemingly unfair outcomes.

If the purpose is to keep the impact on bargaining behavior at a minimum and to achieveresults similar to the no-arbitration treatment in the sense that bargaining types reveal theirdiffering preferences, conventional arbitration may be favored. This kind of safety net can beknitted only at the cost of a modified chilling effect: We observed higher dispute rates whichhad at least in the present experiment no effect on the average payoffs of the two bargainingtypes in comparison to the no-arbitration treatment. However, there must be confidence into

42 This result has consequences for the US where it is particularly emphasized that arbitrators are chosen only ifthey receive support by both parties (see e.g. Bloom and Cavanagh [1986]). Putting this question on the higherlevel of the consent on the arbitration design, CCA may receive a better ranking than FOA.43 Chatterjee and Samuelson [1983] showed that bargaining under incomplete information will not happen in apareto-efficient manner. Charness [2000] showed that there are less costly ways to credibly exchange signals.

25

the arbitrator that he will properly consider the bargaining behavior of the two parties beforemediating between the two impasse offers.

To ensure an even tighter safety net not only excluding disputes but also inducing agreementsaccording to an accepted convention (e.g. an agreement which is charged as fair), the numberof available awards should be restricted to the two final offers. The consequence then is thatthere will be a destiny effect: Splits beyond the convention will be excluded. Bargainers willstop to reveal their own preferences. Again, in such case there must be confidence inarbitrators to prefer the final offer closer to the convention.

Of course, such a purpose induces the question why negotiations should take place at all whenthe outcome is already predetermined. In order to keep the bargaining cost at zero and tomaximize total welfare, negotiations should be forbidden and the pie-splitting determined perdecree. If there is no obvious convention which is accepted by all participants or if there aretwo competing conventions, e.g. of a fair division, it is a disadvantage to restrict the numberof available awards to the two final offers. Suppose e.g. that both parties have the biasedjudgment that the allocation of the complete pie to each of themselves is the only fair outcome(certainly an extreme case).44 If they both demand in their impasse offer the complete pie, thefinal offer arbitrator is in trouble since both offers lead to an unfair outcome for the otherparty. Then, FOA may result in awards which may not be accepted by the negotiators.

Putting it on Occam´s razor, the results of the present study show that the final offerarbitration is an inferior instrument. If there is a convention on pie-splitting this kind ofarbitration design may secure the preferred outcome of negotiations. Then it would be moreefficient to divide the pie per decree according to this implicit agreement. If there is noobvious convention it would be preferable to have arbitrators endowed with a higher numberof available awards than the two final offers of the negotiators.

Last but not least, it should be emphasized that this clear result was deducted from a simplebargaining situation where negotiations had welfare consequences for the bargainers but notfor third parties. For future research it might be interesting to analyze the impact of the twoarbitration designs in more complex situations. Variations can be that the bargaining outcomemight directly affect third parties (in terms of efficiency) or that the negotiators (e.g. unionsand employer associations) simoultaneously bargain about two variables as e.g. wageincreases and working hours per week. Another variation may be that the arbitrators in orderto be able to decide about the award, will need informations which can be influenced by thenegotiating parties. The present discussion shows, however, that the problem of biased

44 Babcock et al. [1995] observed that bargaining parties may have a biased judgment of a fair outcome.

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jugdment will be at the stake as soon as bargaining parties are able to influence theinformation stream. Thus, a hypothesis for the outcome of the latter variation would be thatconventional should be preferred to final offer arbitration.

27

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Study, Econometrica 50, 1123-1142 (1982).Rubinstein, A.: Perfect Equilibrium in a Bargaining Model, Econometrica 50, 97-109 (1982).Siegel, S.; Castellan, N.: Nonparametric Statistics for the Behavioral Sciences. Boston,

McGraw-Hill (1988).Stern, J.L.; Rehmus, C.M.; Loewenberg, J.J.; Kasper, H.; Dennis, B.B.: Final-Offer

Arbitration. Lexington Mass., Heath-Lexington (1975).Stevens, C.M.: Is Compulsory Arbitration Compatible with Bargaining? Industrial Relations

5, 38-52 (1966).Weg, E.; Rapoport, A.; Felsenthal, D.S.: Two-person Bargaining Behavior in Fixed

Discounting Factors Games with Infinite Horizon, Games and Economic Behavior 2, 76-95 (1990).

Wheeler, H.N.: How Compulsory Arbitration Affects Compromise Activity, IndustrialRelations 17, 80-84 (1978).

Wirtz, W.: Address Before National Academy of Arbitrators, Daily Labor Report 23, 1-4(1963).

29

treatment observations ∅ first claim disputes

BR 50 18.0 (69%) 4 (8%)

CCA 50 19.2 (74%) 17 (34%)

FOA 50 17.8 (69%) 7 (14%)

Table 1: Summary of first claims and frequencies of disputes.(For significance of differences see section 4)

treatment ∅ first

claim

∅ impasse

offer of far

bargainer

Numberof equal/unequal

splits

∅ final payoffof far bargainif award/splitis unequal

bargain

periods

BR dispute 22.0 (85%) 16.5 (64%) ------ 00 5.67

BR agree 17.6 (68%) 19/27 15.2 (59%) 3.44

CCA dispute 22.4 (86%) 17.3 (67%) 6/11 15.1* (58%) 4.29

CCA agree 17.6 (68%) 27/6 13.6 (53%) 3.54

FOA dispute 17.8 (69%) 16.8 (65%) (2/5) 11.8♣ (46%) 5.00

FOA agree 17.8 (69%) 39/4 14.0 (54%) 4.09

Table 2: Summary of average offers, payoffs, bargaining periods, and divisions of the pie.*Average payoff of far bargainer if award was according to difference splitting (11 cases)♣Average payoff of far bargainer if award was in favor of close bargainer (5 cases)Final claims and payoffs are displayed as if the pie was of full size, see also Footnote 28

30

First claim BR CCA FOA

-120 1 (2%) 1 (2%) 1 (2%)

121-140 11 (22%) 10 (20%) 7 (14%)

141-165 14 (28%) 4 (8%) 15 (30%)

166-180 2 (4%) 5 (10%) 6 (12%)

181-200 3 (6%) 12 (24%) 11 (22%)

201-220 4 (8%) 3 (6%) 5 (10%)

221-240 11 (22%) 10 (20%) 4 (8%)

241-259 4 (8%) 5 (10%) 1 (2%)

Table 3: Opening claims of bargainer 1 clustered in 8 groups

average payoff

treatment

total size of

pie

Far

bargainer

Close

bargainer

BR 22.5 (87%) 12.2 (54%) 10.3 (46%)

CCA 24.1 12.6 (52%) 11.5 (48%)

FOA 23.7 11.8 (50%) 11.8 (50%)

Table 4: Average amount of payoff for the far and the close bargainer

bargain. periods

treatment

1/2 3 4 5 6 and

more

BR 13 (26%) 12 (24%) 10 (20%) 8 (16%) 7 (14%)

CCA 4 (8%) 22 (44%) 11 (22%) 7 (14%) 6 (12%)

FOA 8 (16%) 11 (22%) 9 (18%) 11 (22%) 11 (22%)

Table 5 : Number of bargaining periods in the BR, CCA and FOA treatment

31

32

Figure 1a: Opening and impasse offers of the 12 matchings of far with close bargainer in theCCA treatment and awards of the conventional arbitrators.

260 + ♣ 259♣ 250

240 + ♣ 238 ♣ 239♠ 245 ♣ 239

♣ 230 ♣ 230 ♣ 235 ♣ 229♣ 235

220 + ♠ 220 ♣ 218♠ 208

♣ 215

200 + ♠ 200♠ 190

180 +×××× 171 ♠ 170 ♠ 170 ♠ 170

160 + ×××× 160 ♠ 165×××× 155 ♠ 155

×××× 144×××× 155 ×××× 149 ×××× 149 ♠ 150 ×××× 150 ×××× 154

140 +♠ 144

×××× 136 ×××× 139♥

130 ♥♦130 ♥♦ 129 ♥♦ 129 ♥♦ 129

♥130 ♥ 129

120 + ♥♦ 119 ♥♦ 119

♥ 129×××× 128

♥♦ 109 ♦ 109 ♦ 109 ♦ 114

100 + ♥♦ 99♦ 94

80 +

60 +4

+5

+4

+3

+3

+3

+4

+4

+3

+4

+4

+3

equal split

number of bargaining periods

demand of far bargaineroffer of close bargainer

♣ opening offer of far bargainer ♠ impasse offer of far bargainer ×××× award of conventional arbitrater♦ opening offer of close bargainer ♥ impasse offer of close bargainer

33

Figure 1b: Opening and impasse offers of the five matchings of far with far bargainer in theCCA treatment and awards of the conventional arbitrators.

260 +

240 + 240

220 + 220

200 +

180 +

160 +

140 + 145 135

120 + 119

100 + 105

80 +

♣ 230

♦ 170

×××× 000

♥ 90

♠ 7060 +

♣ 211

♦ 150

×××× 000

♥ 109

♠ 59

40 +

♣ 240

♦ 141××××

♥ 113

♠ 3420 +

♣

♦×××× 000♥

♠ 70 +

5+5

+8

+5

+6

equal split

number of bargaining periods

demand of bargainer Ioffer of bargainer II

♣ opening offer of far bargainer I♠ opening offer of far bargainer II♦ impasse offer of far bargainer I ♥ impasse offer of far bargainer II×××× award of conventional arbitrater (always equal split)

♣

♦

×××× 000

♥

♠ 19

34

Figure 2: Opening and impasse offers in the FOA treatment. (The award was always theimpasse offer of the close bargainer)

220 –

210 –

200 – ♣ ♦ 200

190 – ♣190

180 – ♣180♦ 175 ♣175

170 – ♣169 ♣169 ♦ 170♣165 ♦ 165

160 – ♦ 160♦ 155

150 – ♦ 150

140 –

130 – ♥ ♠ ♥ ♠ ♥♠ 125

120 – ♥119 ♥ ♠ 120 ♠ 119♠ 115

110 – ♥110 ♠ 112

100 – ♥100

90 –

80 –

70 –

60 –+ + + + + + +3 4 4 6 4 7 7

equal split

number ofbargaining periods

♠ impasse offer of close bargainer♦ impasse offer of far bargainer♥ opening offer of close bargainer♣ opening offer of far bargainer

demand of far bargainer offer of close bargainer

35

Appendix A: Bargaining Record

date: Game Nr:Bargaining record started at: Group Nr: Finished at:

I demand for myself:offer

Nr. byParty I Party II arbitrator Actual size of

pie

1 I259

2 II259

3 I249

4 II239

5 I229

6 II219

7 I209

8 II199

9 I189

10 II179

11 I169

12 II159

13 I149

36

Appendix B: Instructions for Party I:

You take part in a bargaining experiment between two parties, you are party I, the otherperson is party II. There is a pie with a size of 259 Thaler (the experimental currency) and youhave to bargain with the other party about the splitting of the pie. Party II will be selected atrandom from the group of participants in the other room. All pairings are anonymous.

In the first bargaining period you are entitled to make the opening offer where you maysuggest how to divide the 259 Thaler. Party II can either reject or accept your offer. In case ofrejection party II may make a counteroffer. From the third period on you may in odd-numbered and the other party may in even-numbered periods continue to make alternatingoffers. Any further proposal beyond period two induces a shrinking pie of DM 1 per period.After period 1, you are free to make a decision according to one of the following four choices:

1) You make an offer to the other party where you suggest how to split the pie.2) You ask the other party for another offer without making an offer by yourself.3) You accept the last offer of the other party.4) You break down the negotiations [and (in treatment 2 and3) ask for arbitration].

Make a decision according to one of the four choices. Write down your decision into thebargaining record. After making your decision the sheet will be transferred to the other party.

The negotiations will end either if one of the two parties agrees to the splitting of the piesuggested by the other party or if one party decides to break down negotiations. If you succeedto make an agreement, both parties will get paid according to that agreement. If you decide tobreak down negotiations, then

[in treatment 1] both parties will receive no payment at all.

[in treatment 2] you may ask for conventional arbitration. The arbitrator will receive yourbargaining record and will make a decision of his own choice. You have to accept the decisionof the arbitrator. Then you will receive payments according to the award of the arbitrator.

[in treatment 3] you may ask for final offer arbitration. The arbitrator will receive yourbargaining record. The arbirtrator has to choose one of the two final offers as award. You haveto accept the decision of the arbitrator. Then you will receive payments according to the awardof the arbitrator.

Earnings are confidential. Only you and a third person not involved in the experiment willknow the amount you earned. Each experimental thaler is worth 0.10 DM.

37

If you like you may comment your decisions on the back side of this instruction. If at any timeyou have questions or problems, raise your hand and you will be assisted.