Answer Happy

7. Consider the following game: L R U 0,1 1,0 D 4,3 0,5 (a) Argue that this game does not have a pure strategy Nash equilib- rium. (b) Compute the unique mixed strategy Nash equilibrium of this game. (C) Suppose that this game is repeated indefinitely, treating time as discrete, and assuming that players discount future payoffs accord- ing to some factor B E (0,1). Prove that there can exist a subgame perfect Nash equilibrium of this repeated game in which players do not randomize along the equilibrium path; in other words, in the realized outcome, each player's action in each period is a pure strategy of the stage game rather than a mixed strategy of the stage game. (d) Either find a pure strategy subgame perfect Nash equilibrium of this repeated game or prove that no such equilibrium exists.