The self-organizing impact of averaged payoffs on the evolution of cooperation

Abstract: According to the fundamental principle of evolutionary game theory, the more successful strategy in a population should spread. Hence, during a strategy imitation process a player compares its payoff value to the payoff value held by a competing strategy. But this information is not always accurate. To avoid ambiguity a learner may therefore decide to collect a more reliable statistics by averaging the payoff values of its opponents in the neighborhood, and makes a decision afterwards. This simple alteration of the standard microscopic protocol significantly improves the cooperation level in a population. Furthermore, the positive impact can be strengthened by increasing the role of the environment and the size of the evaluation circle. The mechanism that explains this improvement is based on a self-organizing process which reveals the detrimental consequence of defector aggregation that remains partly hidden during face-to-face comparisons. Notably, the reported phenomenon is not limited to lattice populations but remains valid also for systems described by irregular interaction networks.