3. (18 points) 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
2 0
8 2
Bottom
6 3
5 1
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) For each of the following strategy combinations, write TRUE if it is Pareto Efficient, and FALSE if it is not:
i) Top/Left
ii) Top/Right
iii) Bottom/Left
iv) Bottom Right
3. (18 points) 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 | 2 0 | 8 2 | |
Bottom | 6 3 | 5 1 |
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) For each of the following strategy combinations, write TRUE if it is Pareto Efficient, and FALSE if it is not:
i) Top/Left
ii) Top/Right
iii) Bottom/Left
iv) Bottom Right