Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games

We introduce a relaxed Nash equilibrium concept for strategic form games, called quasi-Nash equilibrium, which exists in every diagonally transfer quasi-concave games. The quasi-Nash equilibrium has the property to be stable with respect to perturbations on both payoff functions and mistakes in playing pure strategy profiles. We compare our relaxed equilibrium with the Reny equilibrium (introduced in a recent paper) and give stability properties for the Reny equilibrium.