Efficiency and stochastic stability in normal form games

Abstract

Standard evolutionary game models select the risk-dominant equilibrium, even if it is not efficient. On the other hand, Robson [Robson, A.J., 1990. Efficiency in evolutionary games: Darwin, Nash and the secret handshake. J. Theoret. Biol. 144, 379–396] argues that genes can achieve efficient outcomes with a payoff-irrelevant type, even if such outcomes are not Nash. This paper follows Robsonʼs approach but assumes that a more complex mutation in both the type and the behavior is an order of magnitude less likely than a simpler mutation in only the type or the behavior. In weakly acyclic games, every long-run stable strategy profile is a strict Nash equilibrium. Meanwhile, a Pareto undominated strict Nash equilibrium is stochastically stable if for each player, the opponentsʼ equilibrium action profile uniquely maximizes his payoff given his equilibrium action. These results can be generalized to generic cyclic two-person games. In a common interests game, a strategy profile is selected if and only if it yields the unique Pareto efficient payoff vector.