NASH Equilibrium in Lower Probabilities

Abstract

A Nash equilibrium can be interpreted as a common theory about the players' actions. It is required that the theory is consistent with each player choosing an optimal response to the theory. It is usually required that the theory takes the form of a combination of probability measures on players' strategies. We analyze the effects of relaxing this requirement, allowing the theory to take the form of a lower probability measure, also called a belief function. In particular this allows for a strategy that is never a best reply against probability measures on other players to be part of an equilibrium.