economic game theory confused

Page 1. (24 points) Please state whether each of the following statements is true or false. Explain why the true statements are true. Explain why the false statements are false. (a) Suppose that o* is an evolutionarily stable strategy in polymorphic equilibrium, and let a be an action to which of assigns positive proba- bility. If (a, a) is a pure-strategy equilibrium, then of does not assign positive probability to an action different from a. (b) Every extensive game with imperfect information that has a separat- ing equilibrium also has a pooling equilibrium. (c) The Tit-for-Tat strategy is a best response to any strategy in the infinitely-repeated Prisoner's Dilemma game. (d) An evolutionarily stable strategy in polymorphic equilibrium for a game where each player has two strategies must have that the ex- pected payoff to each strategy is a decreasing function of the propor- tion of other players playing that strategy