Game theory.

Consider the following two-player extensive-form game with perfect infomation. Player 1 moves rst, choosing between actions A and B. Player 2 moves second, choosing between actions 0 and D if player 1 played A, and choosing between actions E and F if player 1 played B. Player 1 makes a nal move: a choice between actions G and H following the history of play (14,0); a choice between I and J after history (A, D); a choice between K and L after history (B, E); a choice between M and N after history (B, F). The payoffs for each path of play are given in the following table: (a) [2 points] Draw the extensive-form representation of this game. (b) [2 points] How many subgames does the game have? How many pure strategies does each player have? (c) [4 points] Solve the game using backward induction. (d) [2 points] Does the game have a Nash equilibrium in which players get payoffs (5, 7)? If yes, construct such an equilibrium. If not, explain why not. For parts (c) and (d), make sure to specify the equilibrium strategies at every decision node