Fall back equilibria

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underlying thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium, and discuss the relations with other Nash equilibrium refinements, in particular proper equilibrium. Furthermore, we show that for bimatrix games fall back equilibrium is a strict concept. We also consider the structure of the set of fall back equilibria for bimatrix games