Cognitively Stable Generalized Nash Equilibrium in Static Games with Unawareness

Abstract

In game theory, recently models and solution concepts of games with unawareness have been developed. This paper focuses on static games with unawareness and points out a conceptual problem of an existing equilibrium concept called generalized Nash equilibrium. Some generalized Nash equilibria can be cognitively unstable in the sense that, once such an equilibrium is played, some agent may feel that the outcome is unexpected one at some level of someone’s perception hierarchy. This may lead to change in the agent’s perception and thus her behavior. Based on the observation, we characterize a class of generalized Nash equilibrium that satisfies cognitive stability so that it can avoid such a problem. Then we discuss relationships between cognitively sable generalized Nash equilibrium and Nash equilibrium of the objective game, that is, how unawareness can or cannot change the equilibrium convention.