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:

left right

top 4 5 1 4

bottom 5 1 3 8

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 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

ii) Player A plays Bottom and Player B plays Left

iii) Player A plays Top and Player B plays Right

iv) 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? (Give your answer in terms of the strategies each player choosesâ€"for example, “Player A plays Bottom and Player B plays Rightâ€)

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