Problem 1 (Two-period game). Consider a two-player two-period game where each period the players play the following simultaneous move stage game: a b 1\2 B C 4,4 1,5 0,0 5,1 0,0 0,0 0,0 0,0 3,3 After the first period the players observe what was played in the first period. The payoff of each player is the sum of the payoffs from the two periods. Throughout the question restrict attention to pure strategies. (a) Find all Nash equilibria in the stage game. (b) Show that there exists a subgame-perfect equilibrium of the entire game such that the players play (B,a) under all circumstances: in the first period, and in the second period regardless of what happened in the first period. (c) Can you find a subgame-perfect equilibrium of the entire game such that players play (A, a) in the first period? Explain your answer. (d) Can you find a Nash equilibrium of the entire game that is not a subgame-perfect equilibrium? Explain your answer. Problem 1 (Two-period game). Consider a two-player two-period game where each period the players play the following simultaneous move stage game: a b 1\2 B C 4,4 1,5 0,0 5,1 0,0 0,0 0,0 0,0 3,3 After the first period the players observe what was played in the first period. The payoff of each player is the sum of the payoffs from the two periods. Throughout the question restrict attention to pure strategies. (a) Find all Nash equilibria in the stage game. (b) Show that there exists a subgame-perfect equilibrium of the entire game such that the players play (B,a) under all circumstances: in the first period, and in the second period regardless of what happened in the first period. (c) Can you find a subgame-perfect equilibrium of the entire game such that players play (A, a) in the first period? Explain your answer. (d) Can you find a Nash equilibrium of the entire game that is not a subgame-perfect equilibrium? Explain your