A Bounded Rationality, Evolutionary Model for Behavior in Two Person Reciprocity Games

Standard non-cooperative game theory is not selective enough to discriminate among many of the possible outcomes in infinitely repeated reciprocity games. However, experimental evidence, especially in symmetric games, suggests strongly that people arrive at only a few outcomes. Theoretical justification for these particular outcomes is usually derived from focal and axiomatic solution concepts, yet these procedures are inherently ad-hoc. Here the outcome of a population game with evolutionary dynamics is examined in order to theatrically justify experimentally observed behavior in a less ad-hoc manner. It is shown that under an assumption of limited rationality, specifically limited memory, there is a unique global equilibrium in the Replicator Dynamics. The unique equilibrium contains a trio of outcomes: non-cooperative Nash play, payoff irrational play, and cooperative turn-taking, which roughly match the outcomes observed experimentally.