Binary action games: Deviation properties, semi-strict equilibria and potentials

Abstract For binary action games we present three properties which have in common that they are defined by conditions on marginal payoffs. The first two properties guarantee the existence of a special type of Nash equilibrium called semi-strict Nash equilibrium, for which we also show an algorithm to locate. The third one guarantees the existence of an exact potential, and can realize the aforementioned two properties in a class of exact potential games. The first one guarantees the existence of a generalized ordinal potential. Each symmetric binary action game possesses all the three properties. The results are illustrated by three applications.