Reference-dependent preferences, super-dominance and stochastic stability

This paper investigates stochastic stability of noisy best response dynamics with reference-dependent preferences. We define a strategy as super-dominant in a 2 × 2 coordination game if it is the maximin strategy in terms of monetary returns and the state that all players play it constitutes an equilibrium which Pareto-dominates all other equilibria. If such a strategy exists, the corresponding equilibrium, which we call the super-dominant equilibrium, is uniquely stochastically stable for the BRM choice rule (the best response choice rule with uniform random errors) given any model of reference-dependent preferences. However, for any 2 × 2 coordination game with a super-dominant strategy, there exists a model of reference-dependent preferences with which the super-dominant equilibrium fails to be stochastically stable for the logit choice rule.