Suppose that two players are playing the following game. Player 1 can choose eit

Question

Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B. Does player 1 have a dominant strategy, and if so what is it? Does player 2 have a dominant strategy and if so what is it? For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not: Top / Left Top / Right Bottom / Left Bottom Right What is Player 1's maximin strategy? What is player 2's maximin strategy? If the game were played with Player 1 moving first and player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?

Explanation / Answer

A. Player 1 does not have a dominant strategy
B. Player 2 does not have a dominant strategy
C. i) Top/Left - TRUE
ii) Top/Right - FALSE
iii) Bottom/Left - FALSE
iv) Bottom/Right - TRUE
D. Player 1's maximin strategy is to play Bottom
E. Player 2's maximin strategy is to play Left
F. Player 1 will choose Top and player 2 will choose Left.

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