On the Relationship between p-Dominance and Stochastic Stability in Network Games

Evolutionary models with persistent randomness employ stochastic stability as a solution concept to identify more reasonable outcomes in games with multiple equilibria. The complexity of computational methods used to identify stochastically stable outcomes and their lack of robustness to the interaction structure limit the applicability of evolutionary selection theories. This paper identifies p-dominance and contagion threshold as the properties of strategies and interaction structure respectively that robustly determine stochastically stable outcomes. Specifically, we show that p-dominant strategies, which are best responses to any distribution that assigns them a weight of at least p, are stochastically stable in networks with contagion threshold of at least p.