On the learning and stability of mixed strategy Nash equilibria in games of strategic substitutes

This paper analyzes the learning and stability of mixed strategy Nash equilibria in games of strategic substitutes (GSS), complementing recent work done in the case of strategic complements (GSC). Mixed strategies in GSS are of particular interest because it is well known that such games need not exhibit pure strategy Nash equilibria. First, we establish bounds on the strategy space which indicate where randomizing behavior may occur in equilibrium. Second, we show that mixed strategy Nash equilibria are generally unstable under a wide variety of learning rules. Multiple examples are given.