The Competitive Ultimatum Game

When Competition Matters, Although It Should Not, and Backward Induction Appears Through the Backdoor

Klaus Abbinkb, Ron Darzivj, Zohar Gilulaj, Harel Gorenj, Bernd Irlenbusche, Arnon Kerenj, Bettina Rockenbache, Abdolkarim Sadrieht, Reinhard Seltenb, and Shmuel Zamirj

University of Bonnb, Hebrew University Jerusalemj, University of Erfurte, Tilburg Universityt

Preliminary version, April 2000. Comments are welcome.

Abstract A game is introduced and experimented that allows for a direct comparison of the two predominant equilibrium concepts of economic theory: the competitive versus the strategic equilibrium. Neither of the two extreme and completely disjoint equilibrium predictions fully explains the data. Observed outcomes, however, are closer to the competitive than the subgame perfect (sequential) equilibrium predictions. As subjects gain experience in repeated plays of the game, outcomes move even closer to the competitive equilibrium. But, within play behavior frequently exhibits patterns that qualitatively correspond to the game theoretic predictions. Thus, although the competitive equilibrium concept clearly is the better predictor of behavior in the given environment, the strategic equilibrium concept also retains some of its behavioral relevance.

Keywords Competition, backward induction, equilibrium concepts, experimental economics

JEL Classification Codes C78, C91, C92, D82

Acknowledg ements The authors thank the teams of the RatioLab at the Hebrew University of Jerusalem and the Laboratorium für experimentelle Wirtschaftsforschung at the University of Bonn for their aid in collecting the data. Many thanks also to the seminar participants at the ENDEAR Bari workshop and summer school (1999) as well as at the IAES meeting in Munich (2000) for many helpful comments. Support by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 303, by the German-Israeli Foundation ! GIF !, by the European Union through the TMR program ENDEAR (FMRX-CT98-0238), and by the Land Nordrhein-Westfalen is gratefully acknowledged.

Correspondence Karim Sadrieh, Dept. of Economics, Tilburg University, POBox 90153, 5000 LE Tilburg, Netherlands - [email protected]

1 1. Introduction

Ever since game theory introduced a new equilibrium concept to economic theory, the game-theoretic strategic equilibrium has co-existed with the traditional competitive equilibrium. The co-existence has been “friendly” in the sense that the followers of neither concept have seriously attempted to extinguish the application of the concept they do not fancy. One reason for this persistent duality lies in the fact that the theoretic delineation of the concepts has proven to be intricate. Not only do both concepts (in principle) allow for multiplicity of equilibria with a given set of assumptions, but both also allow an application to models with a broad range of possible assumptions. Perhaps it is due to these difficulties, that general results concerning the relationship of the strategic and the competitive equilibrium have not been derived so far.

Generally, it seems possible to devise economic institutions in which the two equilibrium concepts produce any constellation of conclusions: equilibrium outcome sets that coincide, equilibrium outcome sets that are disjoint, or equilibrium outcome sets of which one is partially or wholly contained in the other. Clearly, the exciting case for research is the case in which equilibrium predictions do not coincide. In such cases, when the equilibrium concepts are in competition with one another, the problem of comparing and evaluating the conflicting equilibrium concepts emerges. This is the issue that is at the heart of the present paper.

Instead of taking an axiomatic approach to tackle the issue of equilibrium concept evaluation, an empirical approach is attempted with this research. Using the method of experimentation, we study a game in which the set of outcomes predicted by the competitive equilibrium and the set of outcomes predicted by the strategic equilibrium are disjoint. The goal is to evaluate the two equilibrium predictions in terms of their behavioral relevance. Obviously, if one of the equilibrium outcomes predominates our experimental observations, conclusions concerning the behavioral relevance of the concepts in our setting will be apparent. Our design, however, also will allow us to draw more intricate conclusions from the comparison of observed decision paths. Finally, the robustness of the results with respect to changes in the informational setting will be explored by comparing the results of experimental sessions with a perfect to those of sessions with an imperfect information version of the underlying game.

To our knowledge, this is the first systematic experimental study concerned with the evaluation of the competing equilibrium concepts. However, an interesting benchmark for our work is supplied by PRASNIKAR and ROTH (???). Interested in tests of an adaptive learning model, they conducted experiments with a game in which the predictions of the two equilibrium concepts coincide at an extreme outcome. They find that subjects’ behavior rapidly converges to this jointly strategic and competitive equilibrium of the game. In a way, we find this result comforting, since it confirms the behavioral validity of at least one of the two equilibrium concepts. But, since the predicted outcomes fully overlap, it is not clear whether observed behavior is actually driven by competition or by the backward induction logic of the sub-game perfect equilibrium. 2 In the competitive ultimatum game, which is introduced in this paper, the competitive and the strategic equilibrium predictions are separated at the two extreme ends of the range of possible outcomes. In this game, three proposers, one after the other, can make an offer to a single responder. If the responder accepts the first offer for the division of the cake, the game ends. Otherwise, the second proposers makes an offer, and so forth. The third stage of the game, when only one proposer is left, corresponds to a common ultimatum game.

Backward induction implies that the strategic bargaining power of the responder is very limited in this game. Anticipating that the responder will accept any non-negative amount that is proposed in the last stage, the last proposer will offer no more than the smallest money unit. Anticipating this, the one to last proposer will offer no more than two times the smallest money unit. Finally, the backward induction logic predicts that the responder accepts the first proposer’s offer that is no more than three times the smallest money unit. Thus, in subgame perfect (or sequential) equilibrium, the responder receives a tiny piece of the cake, while the first proposer receives almost the entire cake.

From a competitive equilibrium perspective, however, the responder has an extremely strong monopolis- tic position, while the three proposers face sharp competition. Only one of the proposers can succeed. In fact, supposing that the three proposers are three sellers and the responder is a buyer and looking at the corresponding demand and supply curves, we find that the competitive equilibrium price is zero, since the marginal cost of all sellers is zero. Thus, in competitive equilibrium, the responder, who is predicted to receive almost nothing in the strategic equilibrium, receives almost the entire cake, leaving the proposer with close to nothing.

The experiments show that the competitive pressure on the proposers is clearly greater than the bargaining power that the game theoretic reasoning attributes to them. The competition amongst proposers leads to high offers: On average more than half of the cake is offered to the responder. Furthermore, as the subjects gain experience with the game, the offers to the responder tend to rise. The stiff competition pushes first proposer offers from slightly above 50% in the first round to well over 60% in round 35. Since an upward trend in the offers can be clearly seen in 22 of 24 independent subject groups, the conclusion seems justified that observed outcomes develop in the direction predicted by the competitive equilibrium concept, although the competitive equilibrium outcome is not reached.

However, a second strong regularity appears in the data. In general, the observed offers in a game decline as the game enters later stages, going from one proposer to the next. In the last stage, most observed offers are in the range that is typically also observed in ultimatum bargaining experiments. Thus, as the responder’s threat of rejection loses its credibility, because the end of the game comes closer, the proposers' offers drop. It is in this effect that the backward induction reasoning strongly reappears in our data.

3 The rest of the paper is organized as follows. First, in section 2, the competitive ultimatum game is defined precisely and analyzed game-theoretically. Then, after the experimental design is described in section 3, the results are reported in section 4.

2. The Competitive Ultimatum Game

The competitive ultimatum game is an extension of the 'classical' ultimatum game (GÜTH,

SCHMITTBERGER, and SCHWARZE 1982) with three (potential) proposers P1, P2, and P3 and one responder R. The three proposers sequentially propose an allocation of the cake C to the responder.

First, P1 proposes an allocation a1=(x1,C-x1) of C to R, where x1 denotes the proposed payoff for the responder R and C-x1 denotes the own payoff desired by P1. The game ends if R accepts the proposal of P1. Otherwise, if P1's proposal is rejected by R, P2 proposes an allocation a2=(x2,C-x2) of C to R.

If R accepts P2's proposal, the game ends. Otherwise, if R also turns down P2's proposal, it is P3's turn to propose an allocation a3=(x3,C-x3) of C to R. If R accepts the proposal of proposer P3, R receives x3, P3 receives C-x3, and each of both other proposers receives 0. If R rejects all three proposals all four players receive 0.

Suppose that each proposer Pi is completely informed about the proposal(s) of the proposer(s) who have decided before Pi. This competitive ultimatum game with complete information has multiple subgame perfect equilibria. In order to deduce the bounds for the responder's equilibrium payoff, we follow a simple backwards induction argument. If P3 proposes at least the smallest money unit m to R, it is strictly dominant for R to accept. If P3 offers 0, the responder is indifferent between accepting and rejecting the offer. Thus, in every subgame perfect equilibrium P3 either offers 0 or m to R. Anticipating this, it is strictly dominant for R to accept each proposal of P2, which yields at least 2m for R. However, there are also subgame perfect equilibria in which P2 offers 0 or m to the responder and the responder accepts the proposal. Thus, in every subgame perfect equilibrium P2 either offers 0, m, or 2m to R.

Therefore, it is strictly dominant for R to accept each proposal of P1, which yields at least 3m for R.

Moreover, there are also subgame perfect equilibria in which P1 offers 0, m, or 2m to the responder.

Thus, in every subgame perfect equilibrium P1 either offers 0, m, 2m, or 3m to R. Hence, the lower bound for the responder's equilibrium payoff is 0 and the upper bound is 3m.

Now, suppose that each proposer Pi is not informed about the proposal(s) of the proposer(s) who have decided before Pi. This means that the second and third proposer can infer that the responder rejected the previous proposal(s) from the fact that it is their turn to decide. However, they do not know which amount was actually proposed by the previous proposer(s). The competitive ultimatum game with imperfect information has multiple sequential equilibria. Again, we receive an upper bound for the responder's equilibrium payoff by assuming that R will reject a proposal every time he/she is indifferent between accepting and rejecting. Then, in equilibrium, proposer P3 proposes a3=(m,C-m). Proposer P2 proposes in equilibrium a2=(2m,C-2m) and proposer P1 proposes a1=(3m,C-3m). The responder accepts 4 any proposal yielding more than 0. Thus, on the equilibrium path R accepts the proposal (3m,C-3m) of the first proposer and receives a payoff of 3m. This payoff is the upper bound for the responder's equilibrium payoff. Evidently, the lowest equilibrium payoff of R is zero.

3. Experimental Design and Procedure

Using a 2x2 factorial design, the experiment was conducted with the two informational settings at two locations, namely at the University of Bonn (Laboratorium für experimentelle Wirtschaftsforschung) and at the Hebrew University in Jerusalem (RatioLab). In the open treatment all offers were made public. In this setting all players were informed about all proposals that were made, as they were made. In the second informational setting, the covered treatment, proposers were not informed about the proposals made by other proposers. We performed six sessions per treatment at each location. 12 participants took part in one session, which adds up to 144 participants at each location. The experimental software was written using RatImage (ABBINK and SADRIEH 1995). The program was written such that either of the two languages, German or Hebrew, could be selected before the start of the experiment.

The written instructions1 were read aloud by an experimenter. After this, the participants drew cards which determined the cubicles in which they were seated. At the beginning of the experiment, each cubicle had been randomly assigned a role, with nine proposers and three responders in each session. The roles were not changed during the whole session.

The experiment consisted of 36 rounds. Before each round, three proposers and one responder were randomly matched to form a group. Thus, there were three groups of four subjects in each round. The ordering of the three proposers in a group was randomly assigned for each round. It was equally likely for each proposer to become the first, the second, or the third proposer.

The cake size was 1000 points. Allocations were proposed in the form of an offer to the responder, i.e. proposers specified the number of points they were willing offer to the responder. The smallest money unit was a point. Offers were transmitted to the responder. In the open treatment, each offer was also transmitted to the other two proposers. The responder could accept or reject an offer. If the responder rejected the first or the second offer, no payments were made and it was the turn of the next proposer to suggest a division of the 1000 points. If the third offer was rejected, the round ended with no change in the capital balances of the four group members. If the responder accepted an offer, the points were

1 We aimed to give the participants at both places instructions that were as close as possible in terms of contents and wording. We, therefore, first formulated the instructions in English. Then we translated them into German and Hebrew. Different people translated them back into English. The back-translations were compared to the original text. In case of deviations the translations were adjusted. This procedure was repeated until the original instructions and the back- translations showed practically no more differences.

5 added accordingly to the capital balances of the responder and of the proposer who made the offer and the other two proposers received no payoff for this round. Finally, if an offer was accepted, the round ended. After all 36 rounds, subjects were paid their final capital balances with an exchange rate of DM 1 for 400 points and NIS 1 for 200 points2.

4. Results

4.1. Offers

Table 1 shows the frequency of rounds in which the first, second, and third offer were accepted. In the majority of plays (67.9%), the game already ended after the first proposal, because the responder had accepted the first proposer’s offer.

Table 1: Frequency of acceptance at the three stages of the game

Accepted offer Jerusalem Bonn Jerusalem Bonn Total covered Covered Open open 1st proposer 448 (69.1%) 463 (71.5%) 440 (67.9%) 409 (63.1%) 1760 (67.9%) 2nd proposer 132 (20.4%) 139 (21.4%) 140 (21.6%) 147 (22.7%) 558 (21.5%) 3rd proposer 52 (8.0%) 32 (4.9%) 45 (6.9%) 60 (9.3%) 189 (7.3%) none 16 (2.5%) 14 (2.2%) 23 (3.6%) 32 (4.9%) 85 (3.3%) Total 648 (100%) 648 (100%) 648 (100%) 648 (100%) 2592 (100%)

Similar to the standard ultimatum game with a single proposer, the perfect equilibrium outcomes involve payoffs close to zero for the responder in the competitive ultimatum game. However, table 2 shows that in actual play, the competition among proposers brings responders into a much stronger position. The table shows the average offers in the single sessions. The pairs of columns indicate the average offers made by the first, the second, and the third proposer. The first column of each pair shows the average offers made, the second column the average offers that were accepted by the responders. In all four cells, the average first and second mover offers are well above 500. Hence, first and second proposers frequently propose allocations that give themselves less than the equal split.

In 21 of 24 sessions, the average offers have a strictly declining pattern from the first to the third proposer, such that the second proposers' offers are lower than the first proposers', and the third

2 The exchange rates of points to cash were adjusted in the two countries in a way that total earnings were comparable in terms of teaching assistants’ average hourly wage rates at each location. The exchange rate at the time of the experiment were roughly US-$ 0.66 for DM 1 and US-$ 0.31 for NIS 1.

6 proposers' offers are lowest. Only in three sessions, the average second proposer offer is lower than the average first proposer offer. The randomization test for dependent samples rejects the null hypothesis of equally high first and second proposer offers as well as that of equally high second and third proposer offers at a one-tail p of p = 0.016 (JC and BC), p = 0.031 (JO) and p = 0.063 (BO). Obviously, the first proposers' fear of their offers being rejected is greater than the second proposers’ fear, which in turn

Table 2: Average offers in the competitive ultimatum game

first proposer Second proposer Third proposer Session all accepted all Accepted all accepted 1 636.59 689.36 619.32 708.39 422.22 476.92 2 553.71 574.22 523.06 550.00 366.67 400.00 3 615.60 654.46 538.58 595.73 426.47 426.47 J 4 588.19 622.86 526.32 552.00 403.85 427.27 5 622.45 667.38 602.47 626.24 435.71 477.78 6 546.11 552.42 478.46 502.00 233.33 200.00 C 1 575.15 609.11 552.36 564.84 440.00 500.00 2 530.81 541.54 483.39 510.07 416.67 475.00 3 495.31 522.68 446.19 501.82 335.00 407.14 B 4 512.44 526.06 481.68 509.58 404.25 430.10 5 543.15 558.49 494.95 513.00 356.43 420.00 6 542.15 588.85 506.95 528.32 338.00 414.00 1 525.00 538.35 543.97 559.05 325.00 350.00 2 664.86 716.90 630.89 652.71 412.50 516.67 3 630.87 675.93 560.90 614.50 495.43 508.18 J 4 637.04 666.04 592.73 640.00 443.33 486.36 5 657.27 684.36 587.00 694.07 586.88 645.00 6 676.60 744.06 655.20 712.09 502.73 533.00 O 1 520.00 586.31 469.84 542.70 288.50 340.78 2 564.12 596.34 532.04 543.16 438.13 469.76 3 666.34 695.54 634.63 665.69 542.78 630.83 B 4 518.67 552.59 525.08 552.81 400.20 412.50 5 519.00 534.83 522.78 552.37 412.50 562.50 6 614.07 644.27 600.04 636.15 437.37 492.50 C: covered treatment; O: open treatment; B: Bonn session; J: Jerusalem session

Figure 1 shows the frequency distribution of offers for the aggregate data of all treatments and subject pools. Offers from the interval [451..500] are the most frequently made by subjects in all three proposer positions. This holds true, even though the average offers made by first and second proposers are well above 500, but those made by third proposers are well below 500.

7 4.2. Rejection Behavior

Figure 2 shows the average frequency of rejections conditioned on the position of the proposer. Again, note that the data for third proposers are sparse. Nevertheless, it can be clearly seen that offers that provide an equal split of the cake between the single proposer and the responder are typically rejected at the first stage of the game, but rarely rejected at the last stage.

Distribution of Offers 0.5

0.4

0.3

0.2 rel. frequency

0.1

0 0..50 151..250 351..450 551..650 751..850 951..1000 51..150 251..350 451..550 651..750 851..950 offer first second third

Figure 1

Rejection Rates on Offers 1

0.8

0.6

0.4 rel. frequency

0.2

0 151..250 351..450 551..650 751..850 251..350 451..550 651..750 offer

first second third

Figure 2

8 4.3. Do Offers Converge to Equilibrium?

The results of the previous section show that on average, offer behavior is far away from perfect equilibrium play. The question arises whether at least a convergence towards equilibrium can be observed during the play. Figure 3 shows the development of the average first proposer offers over the 36 rounds of play. The graphs do not show a tendency of the first proposer offers to fall. On the contrary, they even rise slightly. Table 3 shows Spearman rank correlation coefficients between the round number and the average first proposer offers for the single sessions (for the second and third proposer, too few observations are available). The coefficients indicate a rising (positive sign) or falling (negative sign) development of the offers over time.

Evolution of First Proposer Offers 700

600

average offer 500

400 0 5 10 15 20 25 30 35 round JC BC JO BO

Figure 3

Table 3: Spearman rank correlation coefficients between round number and average first proposer offer

Session Jerusalem Jerusalem Bonn Bonn Covered Open Covered Open 1 +0.45 +0.47 +0.28 +0.13 2 +0.79 +0.40 +0.45 +0.06 3 +0.77 +0.62 +0.42 +0.75 4 +0.55 +0.53 +0.12 !0.09 5 +0.68 +0.58 +0.01 +0.11 6 +0.10 +0.28 !0.13 +0.79

9 In 22 of the 24 sessions, the average first proposer offers tend to rise. The one-sample randomization test rejects the null hypothesis that positive and negative rank correlation coefficients occur equally likely ! which would be the case if no trend would be present ! at one-tailed significance levels of a < 0.02 (Jerusalem, open and covered), a < 0.10 (Bonn covered), and a < 0.05 (Bonn open). Thus, we can conclude that in all four cells, the average first proposer offer tends to rise.

4.4. Treatment Differences

The two treatments ! covered and open ! differ in the amount of information provided to the proposers. Where in the open treatment the second and third proposers knew the offers that were made at the previous stages (hence they knew which offers had been rejected before), the proposers in the covered treatment only knew that the responder had rejected one or two offers, but not the amount(s) offered. The aggregate first, second, and third proposer offers are larger in the open condition than in the covered condition, with respect to all offers as well as to the accepted ones. We test the null hypothesis of no difference in the offers in the covered and in the open treatment against the hypothesis of larger offers in the open treatment, for pooled data as well as separately for the two subject pools. The following table 3 shows the one-sided significance levels at which the null hypothesis is rejected using the two- sample randomization test.

Table 4: Significant differences in offers between open and covered treatment

first proposer Second proposer third proposer All Accepted All accepted all accepted pooled data a < 0.10 a < 0.10 a < 0.01 a < 0.02 Jerusalem sessions a < 0.10 n.s. a < 0.10 a < 0.10 a < 0.10 a < 0.05 Bonn sessions n.s. a < 0.10 a < 0.05 a < 0.01 n.s. n.s.

In general, the offers in the open treatment tend to be higher. The difference is particularly sharp with respect to the second proposer offers, and less extreme for the first proposers. The third proposer results might be influenced by the very small data basis on which the averages are computed. Since only few plays reached the third stage, the number of observations may be too small for distinct differences to appear. The observation of the amounts that the responder has rejected seems to influence the proposers' offer behavior towards higher offers.

4.5. Subject Pool Differences

Since the experiment was run at two different universities in two different countries, the question arises whether subjects' behavior in the competitive ultimatum game is different in the two subject pools. Table 2 suggests that in both treatments the Jerusalem subjects seem to offer higher amounts. Testing the

10 difference in average offers between the subject pools using the two-sample randomization test confirms this conjecture. We test the null hypothesis of no difference between the subject pools against the hypothesis of higher average offers in the Jerusalem sessions, applying the test to the average offers of the independent sessions. Table 5 indicates the one-sided significance levels at which the null hypothesis is rejected in favor of the alternative hypothesis.

Table 5: Significant differences in offers between the two subject pools

first proposer Second proposer third proposer all Accepted All accepted all accepted pooled data covered treatment a < 0.01 a < 0.02 a < 0.05 a < 0.05 n.s. n.s. open treatment a < 0.05 a < 0.05 a < 0.10 a < 0.05 n.s. n.s.

With respect to the first and second proposer offers, the null hypothesis can be rejected in both condi- tions, for all offers as well as for the accepted ones only. Note again that, the third proposer results might be influenced by the fact that only very few third proposals can be observed. Interestingly, these results seem to contradict those of ROTH, PRASNIKAR, OKUNO-FUJIWARA, and ZAMIR (1991) at first sight. They find a tendency for smaller offers in the Jerusalem subject pool, compared to the results in Ljubl- jana, Pittsburgh, and Tokyo, where in our experiment the Israeli subjects tend to offer higher amounts than the Germans3.

There seems to be a simple explanation for the contradicting evidence: The common denominator seems to be that Israeli subjects are less reluctant to accept unequal allocations, while the difference between the two games lies in the distribution of bargaining power. Since the egalitarian solution ignores any differences in bargaining power, egalitarian considerations conflict with the tendency of the stronger player to exploit his power. The results observed in this study, as well as those obtained by ROTH, PRASNIKAR, OKUNO-FUJIWARA, and ZAMIR (1991), suggest that the Israeli subjects are "tougher" in using a strong position, and less resistant to accept being the weaker player. This coincides with lower offers in the standard ultimatum game, where the proposer is in the stronger position, and higher offers

3 In recent years, several experimental studies comparing behavior in different countries have been conducted. BRANDTS, SAIJO, and SCHRAM (1997) find a much stronger tendency to play according to the equilibrium prediction in a public goods game among subjects in Barcelona, compared to the control groups in Amsterdam, Pittsburgh, and Tokyo. The difference is explained by the larger fraction of economics students in the Barcelona subject pool. LENSBERG and VAN DER HEIDEN (1999) find small, but significant differences in the behavior of Dutch and Norwegian students in a gift exchange game. LOHMANN, USUNIER, and WILLINGER (1999), find significant differences between German and French students in an investment game, in the sense that Germans show more trust to the second mover than French students.

11 in the competitive ultimatum game, where the responder is ! despite the game theoretic prediction ! empirically the stronger player. Subjects in the other countries "stick" more strongly than Israelis to the equal division norm, which in the competitive game, appears to be the equal split between the responder and one proposer4.

This hypothesis is supported by another feature of our data. The rising trend of first proposer offers evident in the data is significantly more pronounced for the Israeli subjects than for the German participants. The Spearman rank correlation coefficients are significantly greater for the Jerusalem subject pool. For the pooled data of all twelve sessions in the single subject pools, we can reject the null hypothesis of equal rank correlation coefficients for both subject pools at a significance level of a < 0.01 (one- tailed). Applied separately to the data for the treatments, we observe higher rank correlation coefficients in the Jerusalem sessions in both treatments, where the difference is significant for the covered treatment (a < 0.02, one-tailed), and not significant for the open treatment. The steeper rise of the average offers, that is observed in the Jerusalem sessions, is consistent with the hypothesis that the subjects in Bonn are more reluctant to depart from the equal division principle and to accept unequal splits. In the first six rounds of the experiment, the offers in the Jerusalem sessions are only slightly ! and insignificantly ! higher than in the Bonn sessions. In both subject pools, the average offers in the first rounds are only little higher than 500. Subjects of both pools seem to start with similar initial perceptions of the game. These seem to be influenced mainly by the equal division principle. In the course of the experiment, the Jerusalem subjects are more willing to quit this principle in favor of the stronger player ! the responder !, where the subjects in Bonn are more reluctant to do so5.

4 Interestingly, the possible alternative fairness norm of an (expected) equal split between all players is empirically irrelevant. Since a single proposer in a group using this scheme receives a payoff only in every third round, offers of 250 would lead to an equal distribution of payoffs among all payoffs over the whole experiment. However, as the figures 2 and 3 show, such offers are rarely made and almost always rejected.

5 One might be tempted to interpret the differences between the two subject pools as a reflection of “cultural” differences between Germany and Israel. However, we are very careful to do that. Of course, our subject pools are not representative of the societies of the two countries. Further, we did not control for an exactly comparable composition of the two subject pools with respect to gender, social background, major, or age. Though both laboratories are located in social science buildings, and hence both subject pools mainly consist of social science students, such differences might be predominant for the differences in behaviour. Thus, our results do not necessarily reflect cultural differences between the two countries.

12 References

ABBINK, Klaus, and Abdolkarim SADRIEH (1995): RatImage - Research Assistance Toolbox for Computer-Aided Human Behavior Experiments. SFB Discussion Paper B-325, University of Bonn. BRANDTS, Jordi, Tatsuyoshi SAIJO, and Arthur SCHRAM (1997): A Four Country Comparison of Spite and Cooperation in Voluntary Contribution Mechanisms. Mimeo, Universitat Autonoma de Barcelona. GÜTH, Werner, Rolf SCHMITTBERGER, and Bernd SCHWARZE (1982): An Experimental Analysis of Ultimatum Bargain- ing. Journal of Economic Behavior and Organization, 3, 367-388. VAN DER HEIDEN, Eline, and Terje LENSBERG (1999): Social capital formation: Some theory and experimental evidence. Mimeo, Tilburg University, The Netherlands LOHMANN, C., J.C. USUNIER, and M. WILLINGER (1999): A comparison of trust and reciprocity between France and Germany : an experimental investigation based on the investment game. Mimeo, University of Strasbourg. ROTH, Alvin E., Vesna PRASNIKAR, Masahiro OKUNO-FUJIWARA, and Shmuel ZAMIR (1991): Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo. American Economic Review, 81, 1068-1095.