Abstract
In this paper, we study a weak prisoner's dilemma (PD) game in which both strategies and update rules are subjected to evolutionary pressure. Interactions among agents are specified by complex topologies, and we consider both homogeneous and heterogeneous situations. We consider deterministic and stochastic update rules for the strategies, which in turn may consider single links or the full context when selecting agents to copy from. Our results indicate that the co-evolutionary process preserves heterogeneous networks as a suitable framework for the emergence of cooperation. Furthermore, on those networks the update rule leading to a larger fraction, which we call replicator dynamics, is selected during co-evolution. On homogeneous networks, we observe that even if the replicator dynamics again turns out to be the selected update rule, the cooperation level is greater than on a fixed update rule framework. We conclude that for a variety of topologies, the fact that the dynamics co-evolves with the strategies leads, in general, to more cooperation in the weak PD game.
Highlights
Evolutionary game theory on graphs or networks has attracted a lot of interest among physicists in the last decade [1, 2], both because of the new phenomena that such a non-hamiltonian dynamics [3] gives rise to and because of its very many important applications [4, 5]
This is the commonly adopted choice in simulations of evolutionary game theory and, some differences have been reported in specific cases with sequential dynamics [39], changes are in general limited to a narrow range of parameters [2, 10, 40], at least for homogeneous networks
In this paper we have largely extended the work on co-evolution of strategies and update rules on square lattices reported in [27]
Summary
Evolutionary game theory on graphs or networks has attracted a lot of interest among physicists in the last decade [1, 2], both because of the new phenomena that such a non-hamiltonian dynamics [3] gives rise to and because of its very many important applications [4, 5]. We address the issue of the lack of universality and the problems it poses for applications to real world problems through the idea of co-evolution The rationale behind this approach is simple: if there are many possibilities regarding networks or dynamics and no a priori reasons to favor one over another, one can take a step beyond in evolutionary thought by letting a selection process act on those features: The types of networks or dynamics that are not selected along the process should not be considered as ingredients of applicable models.
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