In this work we study a weak Prisoner\^as Dilemma game in which bothstrategies and update rules are subjected to evolutionary pressure.Interactions among agents are specified by complex topologies, and we considerboth homogeneous and heterogeneous situations. We consider deterministic andstochastic update rules for the strategies, which in turn may consider singlelinks or full context when selecting agents to copy from. Our results indicatethat the co-evolutionary process preserves heterogeneous networks as a suitableframework for the emergence of cooperation. Furthermore, on those networks, theupdate rule leading to a larger fraction, which we call replicator dynamics, isselected during co-evolution. On homogeneous networks we observe that even ifreplicator dynamics turns out again to be the selected update rule, thecooperation level is larger than on a fixed update rule framework. We concludethat for a variety of topologies, the fact that the dynamics coevolves with thestrategies leads in general to more cooperation in the weak Prisoner's Dilemmagame.
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