Anisotropic strategies and the evolution of cooperation in social dilemmas on networks

Anisotropic strategies are introduced and studied numerically and analytically in the context of prisoner's dilemma (PD) played in a system of connected agents for their effects on the evolution of cooperation. For an agent competing with k neighbors, an anisotropic strategy has k entries representing the different actions against each of the opponents. The commonly used cooperative and non-cooperative strategies against all opponents are isotropic and special cases of anisotropic strategies. For evolutionary PD based on a death-birth process in dynamically formed competing groups, selection results in a totally non-cooperative state but the dynamics is altered by the anisotropic strategies. For agents connected by static networks having a uniform degree, the cooperative level exhibits plateaux as the temptation payoff increases. The plateaux represent the dominance of different classes of anisotropic strategies with decreasing cooperative entries. Dynamical equations with results in good agreement with simulation results on the evolution of strategies and the long time behavior are constructed. For static networks with a spread in degrees, the plateaux disappear except for the one corresponding to a totally cooperative population. For all cases, anisotropic strategies are found to maintain a cooperative level no less than that in a corresponding system in which only isotropic strategies are in play for high temptation payoffs. Anisotropic strategies suggest an alternative mechanism for enhancing cooperation in PD and other games that is worthy of further investigations.