Cooperation enhanced by indirect reciprocity in spatial prisoner’s dilemma games for social P2P systems

Abstract

Abstract With the growing interest in social Peer-to-Peer (P2P) applications, relationships of individuals are further exploited to improve the performances of reputation systems. It is an on-going challenge to investigate how spatial reciprocity aids indirect reciprocity in sustaining cooperation in practical P2P environments. This paper describes the construction of an extended prisoner’s dilemma game on square lattice networks with three strategies, i.e., defection, unconditional cooperation, and reciprocal cooperation. Reciprocators discriminate partners according to their reputations based on image scoring, where mistakes in judgment of reputations may occur. The independent structures of interaction and learning neighborhood are discussed, with respect to the situation in which learning environments differ from interaction networks. The simulation results have indicated that the incentive mechanism enhances cooperation better in structured peers than among a well-mixed population. Given the realistic condition of inaccurate reputation scores, defection is still successfully held down when the players interact and learn within the unified neighborhoods. Extensive simulations have further confirmed the positive impact of spatial structure on cooperation with different sizes of lattice neighborhoods. And similar conclusions can also be drawn on regular random networks and scale-free networks. Moreover, for the separated structures of the neighborhoods, the interaction network has a critical effect on the evolution dynamics of cooperation and learning environments only have weaker impacts on the process. Our findings further provide some insights concerning the evolution of collective behaviors in social systems.