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 5
|
9 4
|
|
|
Bottom
|
7 4
|
5 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, write 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 discussed in the class notes, what strategy will each player choose?