On proper refinement of Nash equilibria for bimatrix games

In this paper, we introduce the notion of set of ϵ -proper equilibria for a bimatrix game. We define a 0–1 mixed quadratic program to generate a sequence of ϵ -proper Nash equilibria and show that the optimization results provide reliable indications on strategy profiles that could be used to generate proper equilibria analytically. This approach can be generalized in order to find at least one proper equilibrium for any bimatrix game. Finally, we define another 0–1 mixed quadratic program to identify non-proper extreme Nash equilibria.