 games: the classic ultimatum games and the “multi person market behaviour” game. In the second game, proposers have to compete each other: there is n-1 proposers (n participants) who concurrently propose an offer to responder. Needless to mention, the responder has the opportunity to consider the highest offer. If there are more than one proposers offer the highest offer, one of them is randomly selected. Once again, if self-interest hypothesis was observed, in the classic ultimatum game, the proposers were expected to virtually get all gains from trade while in the market game, the situation will be reversed and the responder will get the most out of 1000 tokens. Knowing that the responder will only accept the highest offer, proposer knew that he would earn no return if his offer is less than the others. Therefore, all of the splits will be raised up as high as possible, as long as he still earn something which was considered to be fair. Theoretically, there will be a unique sub-game perfect equilibrium outcome when at least two proposers make an offer of all tokens and then the responder gets all from the trade.
Different modes of games bring back different kind of results. The first game reflects the differences in the social norm “fairness” of each society while the second was meant to test whether the story will be different when the responders have more market power. The data collected from experiment in bargaining environment was consistent with the classic game, when it deviated strictly from the perfect equilibrium and proposals are much nearer the middle of the range. In the market environment, the outcomes were observed to converge quickly to the Nash equilibrium and do not deviate once it has been achieved.
Figure 1: Game with proposer competition – Market Data
Source: Roth et al (1991:1080-1081)
From the figure 1, we can see that after few periods, all four markets in four countries reached to the sub perfect equilibrium and stay there after that. People try different strategies in the early rounds and then quickly come to the same solution to offer nearly all of the tokens to the responders. For example, in Japan case, market outcome changed significantly from about 40% proposers offered lower than 800 tokens in round 1 to nearly 5% who offered that amount in round 10. The same situation can also be observed in Yugoslavia, Israel and US. In other words, the empirical results are quite consistent with the data from the standard ultimatum game.
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The ultimatum game issue didn’t stop here as our economists wanted to study more about the effect of competition on social preferences. Fischbacher et al. (2009) introduced three treatments to the participants to assess the impacts of competitions on the responders’ side. The first treatment was similar to the standard two-player ultimatum game (BG). The second treatment (RC2) added one more responder into the game and the number of responders in the third treatment (RC5) is five. In these treatments, the structure of the game are quite similar to the standard ultimatum game except that there is more than one responders in RC2 and RC5. Now, the proposers were asked to divide their 100 units of money to the responders and the responders have to make the decisions without knowing the choices of others. In the event that all responders reject, all participants earn zero. The prediction about the outcome of these treatments with purely selfish preferences is straightforward and all responders are expected to accept any offer with a positive amount. Once again, there would be a subgame perfect equilibrium outcome when the proposer offer zero and that is still accepted by at least one responder. In the end, the game progressed in the same way as it did in 1982 in Guth’s experiment. Figure 2 will provide us a glimpse over the results of all three treatments.
Fig