The evolution of cooperation in heterogeneous networks when opponents can be distinguished

Cooperation has been widely studied in the context of evolutionary games on graphs. Usually the players are set on the nodes of a network and adopt the same strategy, cooperation or defection, against all of their neighbors. In heterogeneous networks, it was shown that cooperation is highly sustained, although when the cumulative payoff is normalized by the connectivity, the cooperation is severely weakened. Here, we study the evolution of cooperation in heterogeneous networks when it is possible to adopt different strategies against different opponents. We study numerically different types of heterogeneous networks, including scale-free networks, that differ in the extent of the role of the highly connected nodes, usually called hubs. The remarkable result is that cooperation is maintained irrespective of whether the payoff is the total one or the normalized one, and, in spite of such blindness, we still find that the topology has a strong effect. When the presence of the hubs is more prominent, we find that the cooperation level decreases for synchronous update but remains almost unchanged for the asynchronous update. It is also shown that cooperation is robust against errors in the update rule. PACS numbers: 89.65.−s, 87.23.−n, 02.50.Le