Evolving aspirations and cooperation

A model of "satisficing" behavior in the repeated Prisoners Dilemma is studied. Each player has an aspiration at each date, and takes an action. [S]he switches from the action played in the previous period only if the achieved payoff fell below the aspiration level (with a probability that depends on the shortfall). Aspirations are updated in each period, according to payoff experience in the previous period In addition, aspirations are subjected to random perturbations around the going level, with a small "tremble" probability. For sufficiently slow updating of aspirations, and small tremble probability, it is shown that in the long run both players cooperate most of the time.