Another Paper on Ultimatum Games.This Time: Agent Based Simulations
People often don't behave like economic theory predicts them to do. An example for this is the well known ultimatum game, where theoretical results concerning 'rational behavior' deviate greatly from results of laboratory experiments. The paper tries to find out which forces cause the results of experiments and theoretical results for the same game to differ in such a dramatic extend as they apparently do. For this aim, a number of different agent based two population simulations are carried out, resembling the structure of Samuelson's (1997) theoretical work. The first of the two populations involved consists of proposers, i.e. agents offering some amount of money to their opponents. A proposer's strategy is completely characterized by the amount of money she plans to propose. The second population consists of responders, i.e. agents accepting or refusing the offer they get from their opponents. A responder's strategy will be characterized by her threshold, which is the minimum amount she will accept. Confronted with an offer lower than her threshold, a responder will refuse. The game simulated consists of two stages repeatedly entered. During the first stage, the playing mode, the members of the proposers' population are randomly matched with members of the responders' population in order to play a one shot ultimatum game. This procedure is repeated several times in order to let agents gather some experience with their current strategies. After that, the second stage is entered, which is the learning mode. During learning, agents update their strategies by learning by imitation or learning by experiments. After that, another playing mode is entered, etc. There are two benchmark results to the ultimatum game. The first is the theoretical result for one shot ultimatum games, stating that proposers will offer the minimum amount possible and responders will accept. The second benchmark is the result of laboratory experiments stating that proposers will offer one third of the maximum amount. One result of the agent based simulations is the fact, that after some rounds of playing and learning, proposers will end up offering between 10 and 15% of the maximum amount and responders will accept. This result deviates from both, the theoretical as well as the experimentally gained results. In further experiments, it can be found that there are some forces that can remarkably change this outcome: 1. The form of replication plays a very important part: The more elitist a selection scheme is, the closer is the result to the theoretical one. For a selection scheme resembling replicator dynamics, results are closer to the experimental outcomes. 2. Of course, the form of the utility function of both, proposers and responders, is of great importance. Whereas the special form of the function does not affect the outcome very much, the introduction of altruism remarkably changes the results. The question still worked at in the moment is what form and what degree of altruism is needed in order to make the agent based simulations reproduce the results of laboratory experiments. Altogether, the paper presents a number of simulations of a repeated two population ultimatum game in order to find out more about the causes and influences on people's motives and behavior in ultimatum cases.
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