Stochastic Dominance and Generalized Risk-Dominance for 2×2 Coordination Games

Abstract

We provide a generalization of risk-dominance based on an elementary type of stochastic dominance vis-a-vis the uniform probability distribution function, to partially resolve the conflict between pay-off dominance and risk-dominance in coordination games. Such a generalization, unlike risk-dominance, is compatible with equilibrium action profile in coordination games like “battle of the sexes”. Our generalization allows players to conjecture the choice of randomization by the other player, that includes but is not restricted to the uniform distribution function.