The von Neumann–Morgenstern stable sets for the mixed extension of 2×2 games

This paper studies the von Neumann–Morgenstern (vNM) stable sets for the mixed extension of 2×2 games when only single profitable deviations are allowed. We show that games with a strict Nash equilibrium have infinite vNM stable sets, and games without a strict Nash equilibrium have just a unique vNM stable set. A characterization of the strategy profiles that belong to the vNM stable sets is provided. We also show that in games without a strict Nash equilibrium the vNM stable set always contains a Pareto optimal strategy profile.