Coordination and Equilibrium selection in mean defined supermodular games under payoff monotonic selection dynamics

This paper introduces the class of mean defined supermodular games. The characteristic feature of these games is that, given an order on the strategy sets of the players, the payoff to each player depends on his own strategy and the average of the population play. We characterise the set of the Nash equilibria and analyse their dynamic properties under payoff monotonic selection dynamics. Weak Nash equilibria, both in pure and mixed strategies, are unstable. The only asymptotically stable equilibria of the game are symmetric strict equilibria where each player uses the same strategy. We show that the strategies that do not survive the process of iterated deletion of strictly dominated strategies vanish in the long run. As a corollary to this latter result, we show that if the game is dominance solvable then the dynamics converges from any initial interior state.