1. Game Theory Concepts, True or False: Answer if the following statements are true or false. If they are false, give an example that contradicts the statement!

(a) If a symmetric stage game is repeated indefinitely often, all players will have the same payoffs in any equilibrium.

(b) In every subgame-perfect equilibrium of a repeated game, the players are playing a Nash equilibrium of the stage game in every round.

(c) In every repeated game, playing the same stage-game Nash equilibrium in every round of the game is a subgame-perfect equilibrium.

(d) In any SPE of the finitely repeated prisoners dilemma, the players always defect on the equilibrium path.

(e) In any game with incomplete information, each player may not know her opponents payoffs but still knows her own payoffs as a function of the action profile.

A game is symmetric if every player has the same strategy set and the same payo function.