Cooperation in aspiration-based N -person prisoner's dilemmas.

We propose a mathematical model of the N -person prisoner's dilemma game played by a continuous population of agents with a time-dependent aspiration level. The model-a system of differential equations-takes into account the evolution of the aspiration level and of the mean frequency of the cooperators in the population. The dependence of the asymptotic level of cooperation on the individual payoffs and on the transition rates determining the agent's reaction to the received payoffs is studied. In general the existence and the magnitude of the asymptotic level of cooperation depends on N , the payoffs and the transition rates, and decreases with increasing N .