Question5 10 points 24 3 6 67 73 92 81 45 5 4 Consider the e

Question5 10 points 2.4 3, 6 6,7 7,3 9,2 8,1 4,5 5, 4 Consider the extensive form game above. The game has 7 for Player 2. In the backward induction equilibrium in pure strategies. Player 2 gets a payoff of 3 proper subgames. The strategy profile (AGJKM, CF) leads to a payoff of s for Player 1 and 7 (Please, enter only numerical values like:0 1,2 3 ).

Solution

A subgame is a subset of any game that includes initial node which is independent from any information set and successor nodes with in the extensive from of game except the game itself.

A proper subgame is a subset of a game that includes initial node and the nash equilibrium within the tree of the game.

Hence the above game has 3 proper subgames

(AGJKM,CF) would lead to a payoff of 6 for Player 1 and 7 for Player 2 as A->C->G->F->M

If Player 1 playes N to get highest payoff of 8 and Player 2 will get 1 which is less than any payoff player 2 would have earned if player 2 have played E hence Player 2 will always pllay E. Now Player 1 knows Player 2 will play E therefore player 1 will not play G he will play H to get payoff 7, PLayer 2 knows if he plays D then player 1 will play I and PLayer 2 will have payoff of 2 that is less than payoff 3 he will have earned after H therfore PLayer 2 wont deviate and play C and Player 1 H

Player 2 gets payoff of 3