Convergence of aspirations and (partial) cooperation in the Prisoner's Dilemma

This paper proposes an aspiration-based model for (anonymous) cooperation where a large population of agents are re-matched every period to playa Prisoner's Dilemma. At each point in time, agents hold a certain common aspiration level which is updated on the basis of population-average experience. On the other hand, those agents who (relative to current aspiration) feel "dissatisfied" switch actions at a rate which is increasing in the magnitude of the dissatisfaction. The induced process is shown to converge in the long run under quite general conditions. Moreover, if agents are responsive enough, the long-run social state is seen to display some extent of cooperation, a constant positive fraction of the population (always less than halt) choosing to cooperate in every period.