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

Question

Suppose that two players are playing the following game. Player A can choose either Top or Bottom, and Player B can choose either Left or Right. The payoffs are given in the following table:

Player A is the number on the left for the payoff

Player B is the number on the right for the payoff

A) Does Player A have a dominant strategy and if so, what is it?
B) Does Player B have a dominant strategy and if so, what is it?

C) For each of the following: True if the strategy combination is Nash Equilibrium; False if it is NOT a Nash Equilibrium

1. Player A plays Top and Player B plays Left

2. Player A plays Bottom and Player B plays Left

3. Player A plays Top and Player B plays Right

4. Player A plays Bottom and Player B plays Right

D) If each player plays her maximin strategy, what will be the outcome of the game?

Answer must be in terms of the strategies each player chooses (ex: Player A plays bottom and Player B plays Right)

E) Now suppoe the same game is played with the exception that Player A moves first and Player B moves second. Using the backward induction method, what will be the outcome of the game?

Explanation / Answer

Player A has bottom as the dominant strategy.

Player B does not have a dominant strategy.

False. Player A will defect

False. Player B will defect

False. Player A will defect

True

Player A plays Bottom and Player B plays Right

Player A plays Bottom and Player B plays Right

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