Stochastic stability in games with multiple populations: Theory and application

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In stochastic stability/evolution analysis, while single-population models have been developed well, they are not very good at dealing with many-person and/or asymmetric games. In contrast, multiple-population models can easily accommodate those games. Our research project aims to develop stochastic stability analysis based on multiple-population models.In particular, we consider the formation and long-run stability of cooperative groups in a social dilemma situation where the pursuit of individual interests conflicts with the maximization of social welfare. The adaptive play model is applied to a game of group formation where voluntary participants negotiate for an institution to enforce them to cooperate. For a class of group formation games with two types, the stochastically stable equilibrium can be characterized in terms of the Nash products of the associated hawk-dove games, which summarize the strategic interaction among the individuals in the game.