1. Prove that in a two-player strategic-form game, the minmax value in mixed strategies of a player equals his maxmin value in mixed strategies.
2. Suppose that the following game has a unique equilibrium, given by a completely mixed strategy
Answer the following questions:
(a) Prove that the payoff of each player at this equilibrium equals his maxmin value in mixed strategies.
(b) Compute the equilibria in mixed strategies and the maxmin strategies in mixed strategies of the two players. Did you find the same strategies in both cases?