Coexistence of fraternity and egoism for spatial social dilemmas

We have studied an evolutionary game with spatially arranged players who can choose one of the two strategies (named cooperation and defection for social dilemmas) when playing with their neighbors. In addition to the application of the usual strategies in the present model the players are also characterized by one of the two extreme personal features representing the egoist or fraternal behavior. During the evolution each player can modify both her own strategy and/or personal feature via a myopic update process in order to improve her utility. The results of numerical simulations and stability analysis are summarized in phase diagrams representing a wide scale of spatially ordered distribution of strategies and personal features when varying the payoff parameters. In most of the cases only two of the four possible options prevail and may form sublattice ordered spatial structure. The evolutionary advantage of the fraternal attitude is demonstrated within a large range of payoff parameters including the region of prisoner's dilemma where egoist defectors and fraternal cooperators form a role-separating chessboard-like pattern.