Convergence of aspirations and (partial) cooperation in the prisoner's dilemma

This paper proposes an aspiration-based dynamic model for cooperation where a large population of agents are matched afresh every period to play a Prisoner's Dilemma. At each point in time, agents hold a common aspiration level which is updated on the basis of some 'population statistic', i.e. a certain scalar summary (e.g. average payoff) associated to the current state. On the other hand, those agents who feel 'dissatisfied' (relative to current aspiration) switch actions at a rate which is increasing in the magnitude of the dissatisfaction. The resulting process is shown to converge in the long run under quite general conditions. Moreover, if agents are responsive enough, the long-run social state displays some extent of cooperation, with a constant positive fraction of the population (always less than half) choosing to cooperate in every period.