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:

Player 2

Player 1 Left Right
Top 6 2 2 1
Bottom 1 0 0 3

where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.

A) Does player 1 have a dominant strategy, and if so what is it?

B) Does player 2 have a dominant strategy and if so what is it?

C) For each of the following strategy combinations, prepare TRUE if it is a Nash Equilibrium, and FALSE if it is not:

i) Top/Left

ii) Top/Right

iii) Bottom/Left

iv) Bottom Right

D) What is Player 1's maximin strategy?

E) What is player 2's maximin strategy?

F) 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?