q-Strategy spatial prisoner?s dilemma game

We generalize the usual two-strategy prisoner?s dilemma game to a multi-strategy game, in which the strategy variable s is allowed to take q different fractional values lying between 0 and 1. The fractional-valued strategies signify that individuals are not absolutely cooperative or defective, instead they can adopt intermediate strategies. Simulation results on 1D and 2D lattices show that, compared with the binary strategy game, the multi-strategy game can sustain cooperation in more stringent defective environments. We give a comprehensive analysis of the distributions of the survived strategies and we compare pairwise the relative strength and weakness of different strategies. It turns out that some intermediate strategies survive the pure defection because they can reduce being exploited and at the same time benefit from the spatial reciprocity effect. Our work may shed some light on the intermediate behaviors in human society.     

On exploring the genetic algorithm for modeling the evolution of cooperation in a population

In this paper, we propose a genetic algorithm approximation for modeling a population which individuals compete with each other based on prisoner’s dilemma game. Players act according to their genome, which gives them a strategy (phenotype); in our case, a probability for cooperation. The most successful players will produce more offspring and that depends directly of the strategy adopted. As individuals die, the newborns parents will be those fittest individuals in a certain spatial region. Four different fitness functions are tested to investigate the influence in the evolution of cooperation. Individuals live in a lattice modeled by probabilistic cellular automata and play the game with some of their neighborhoods. In spite of players homogeneously distributed over the space, a mean-field approximation is presented in terms of ordinary differential equations.     

Evolutionary prisoner’s dilemma games with local interaction and best-response dynamics

This paper studies the long run behavior in evolutionary prisoner’s dilemma games. All players are assumed to sit around a circle and to interact only with their neighbors. It is known that full-defection is the unique long run equilibrium as the probability of players’ experimentation (or mutation) tends to zero in the best response dynamics. Here, it is shown that full-cooperation could emerge in the long run if one also cares for his neighbors in the bestresponse dynamics.