Rational Constraints and the Evolution of Fairness in the Ultimatum Game

Behavior in the Ultimatum Game has been well-studied experimentally, and provides a marked contrast between the theoretical model of a self-interested economic agent and that of an actual human concerned with social norms such as fairness. How did such norms evolve, when punishing unfair behavior can be costly to the punishing agent? The work described here simulated a series of Ultimatum Games, in which populations of agents earned resources based on their preferences for proposing and accepting (or rejecting) offers of various sizes. Two different systems governing the acceptance or rejection of offers were implemented. Under one system, the probability that an agent accepted an offer of a given size was independent of the probabilities of accepting the other possible offers. Under the other system, a simple, ordinal constraint was placed on the acceptance probabilities such that a given offer was at least as likely to be accepted as a smaller offer. For simulations under either system, agents’ preferences and their corresponding behavior evolved over multiple generations. Populations without the ordinal constraint came to emulate maximizing economic agents, while populations with the constraint came to resemble the behavior of human players.