Even though it is often costly to engage in cooperative behavior, we observe cooperation in many biological and social systems. Some of the mechanisms that have been proposed to answer why this may be, include punishment, reciprocity, and reputation . These mechanisms differ in their details, but they are similar in that some individuals observe the behaviors of their peers and use this information to decide how to behave in the future. It is often assumed that if there are such discriminating individuals, they have perfect information. Even so, the presence of discriminators is not always sufficient to prevent defectors from invading the population. This leaves us with two main research questions. First, is it possible for discriminators to stabilize cooperation? Second, how does this depend on how much information the discriminators store and use?
I studied the dynamics of a population consisting of three interaction types—cooperators, defectors, and discriminators—using standard replicator equations. The agents play several rounds of the donation game. The cooperators always donate, the defectors never donate, and the discriminators donate only to those agents who they believe to have to be good. The discriminators can observe some fraction of the other agents and remember these observations probabilistically. After several rounds of the game, each agent receives a payoff that depends on how many donations he gave and received. Each interaction type, then, will have an expected payoff, averaged over all of the agents of that type. These expected payoffs determine how the frequencies of the three types change over time.
When the discriminators have perfect information, depending on the initial frequencies of the three types, there are two possible outcomes. If there are few discriminators, eventually the population will be made up entirely of defectors. If there are sufficiently many discriminators, on the other hand, the population will eventually exhibit cyclical fluctuations in which all three interaction types are present. The model is somewhat robust to imperfect information: if the discriminators only observe some fraction of the games and only remember some fraction of those observations, it is still possible for the population to cyclically fluctuate with all three interaction types present. But if the discriminators observe too few agents or remember too few of their observations, defection will always dominate. However, if the discriminators are less likely to observe other interaction types than they are to observe themselves and the frequency of discriminators is high enough, it is possible for there to be a stable mix of cooperators and discriminators, which the defectors cannot invade. Thus, by reducing the information that the discriminators have about the other types of agents, cooperation can be stabilized.
 Nowak MA (2006). Five rules for the evolution of cooperation. Science 314: 1560-1563.
 Nowak M & Sigmund K (1998). Evolution of indirect reciprocity by image scoring. Nature 393: 573-577.
Eleanor Brush of Princeton University, USA, is an American citizen. She was funded by IIASA's US National Member Organization and worked during the YSSP in the Evolution and Ecology Program (EEP) with a special emphasis on complex networks.
Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.
Last edited: 19 August 2015
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