1. Consider a game in which Player 1 first selects between L and R. If Player 1
ID: 1146405 • Letter: 1
Question
1.
Consider a game in which Player 1 first selects between L and R. If Player 1 selects L, then players 1 and 2 play a prisoner’s dilemma game represented in the strategic form above. If Player 1 selects R then, Player 1 and 2 play the battle-of-the-sexes game in which they simultaneously and independently choose between A and B. If they both choose A, then the payoff vector is (4,4). If they both choose B, then the payoff vector is (2,2). Finally, if one chooses A while the other B then the payoff vector is (0, 0). The game has _____ proper subgames. Player 1 has _____ pure strategies and Player 2 has _____ pure strategies. (Please, enter only numerical answers like: 1, 2, 3, ...)
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2. Consider the extensive form game above. The game has ______ proper subgames. The strategy profile (AGJKM, CF) leads to a payoff of ______ for Player 1 and ______ for Player 2. In the backward induction equilibrium in pure strategies. Player 2 gets a payoff of ______ (Please, enter only numerical values like: 0, 1, 2, 3,....).
Player II C 6,6 1,7 D 7,1 3,3 Player IExplanation / Answer
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
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