Universal Stochastic Dominance and Equilibrium Selection in Imitation Dynamics

We propose a new dominance concept for n n symmetric normal form games called universal stochastic dominance. This concept is equivalent to risk dominance in 2 2 coordination games but is stronger than 1 2-dominance in coordination games with more than two strategies. In a large class of imitation dynamics, universally stochastically dominant strategies are always selected whereas inferior strategies can be iteratively deleted to eliminate strategies that are never selected. These criteria are respectively su ¢ cient and necessary for stochastic stability and depend only on the payo ¤ matrix of a game. Our results partially characterize the stochastically stable set in a large class of imitation dynamics using conditions that do not require the computation of a stochastic potential function