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

PLAYER B

Does Player A have a dominant strategy? If so, what is it?

Does Player B have a dominant strategy? If so, what is it?

For the next four questions, you’ll be asked whether a strategy combination is a Nash equilibrium or not. Player A plays Top and Player B plays Left

Player A plays Bottom and Player B plays Left

Player A plays Top and Player B plays Right

Player A plays Bottom and Player B plays Right

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

Now suppose the same game is played with the exception that Player A moves first and Player B moves second. Using the backward induction method discussed in the online class notes, what will be the outcome of the game?

Explanation / Answer

We are allowed to do 4 subparts question at a time. Post again for more subparts of question.

A) Does player A have a dominant strategy, and if so what is it?
No

B) Does player B have a dominant strategy and if so what is it?
Yes, right

C) For each of the following say True if the strategy combination is a Nash equilibrium, and False if it is not a Nash equilibrium:

i) Player A plays Top and Player B plays Left
False

ii) Player A plays Bottom and Player B plays Left
False

iii) Player A plays Top and Player B plays Right
True

iv) Player A plays Bottom and Player B plays Right
True

D) If each player plays her maximin strategy what will be the outcome of the game? (Give your answer in terms of the strategies each player chooses)
There is no NE but the mixed strategy is depends on who plays first. Player 2 will always choose right and player 1 will choose bottom if he goes first and top if second

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