ESSs and mixed strategy equilibria:-

Generalize the argument that no ESS in the game in Figure 1 assigns positive probability to AP or to PA, to show the following result.

Let (α∗, α∗) be a mixed strategy equilibrium; denote the set of actions to which α∗ assigns positive probability by A∗.

Then the only strategy assigning positive probability to every action in A∗ that can be an ESS is α∗.