Aspiration-based full cooperation in finite systems of players

We propose a mathematical model of evolution of a finite well-mixed population of players who change their behavior if the payoff obtained from Prisoner’s Dilemma based interactions is smaller than a threshold (aspiration level). The threshold can be a fixed constant or a dynamical variable, which depends on some overall dynamically changing characteristics of the system. We investigate the dependence of full cooperation on the group size, game payoffs, aspiration level, and heterogeneity of the system. For endogenous aspirations we find analytically conditions which guarantee full cooperation in the long run for all initial configurations and group sizes. The result is robust to a stochastic choice of strategies by the heterogeneous players, as documented by numerical simulations.