Note on State Dependent Mutations as an Equilibrium Refinement Device

This note focuses on the use of utility monotonic perturbations as a means of modelling the mutation process in evolutionary models. We show that a game has a detailed balanced and utility monotonic perturbation if and only if it is an ordinal potential game. We also show that utility monotonicity is not strong enough to serve as an equilibrium refinement device for ordinal potential games. An equilibrium refinement device that is applicable to a general class of games must, therefore, satisfy a stronger utility monotonicity condition while the detailed balance condition can no longer hold. We believe that a tightening of the bounds on the magnitude of stationary distributions could substantially further research in this topic.