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Contagion, Network Cohesion and Long Run Stability in Evolutionary Games

This paper studies how the network structure affects the long-run equilibria emerging in coordination games when agents are myopic best responders. Our analysis builds-on the properties of the process of contagion. We demonstrate that when contagion is feasible, the network diameter, a measure of the cohesiveness of the network, determines the uniqueness of long-run equilibria. The maximum group cohesion is one of the network measures that determines the feasibility of contagion. We show that for regular cyclic networks, there exists a threshold network diameter above which strategies in the smallest iterated p-best response set, for p equal to the maximum group cohesion, are uniquely stochastically stable. We discuss how these results can be extended to evolutionary dynamics on arbitrary networks using different network measures that determine the feasibility of contagion.