Suppose that two players are playing the following game. Player A can choose either Top or Bottom and Player B can either choose Left or Right. The payoffs are given in the following table where the number on the left is payoff to Player A, and then number on the right is the payoff to Player B.

Player B

Left Right

Top 4 5 1 4

Player A Bottom 5 1 3 8

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

a) top is a dominant strategy for Player A

b) bottom is a dominant strategy for Player A

c) both of these

d) none of these

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

a) left is a dominant strategy for Player B

b) right is dominant strategy for Player B

c) both of these

d) none of the above

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

a) this is not a equilibrium

b) this is not a nash equilibrium

Player A plays Bottom and Player B plays Left

a) this is not a equilibrium

b) this is not a nash equilibrium

Player A plays Tops and Player B plays Right

a) this is not a equilibrium

b) this is not a nash equilibrium

Player A plays Bottom and Player B plays Right

a) this is not a equilibrium

b) this is not a nash equilibrium

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

a) Player A plays Tops and Player B plays Left

b)Player A plays Bottom and Player B plays Left

c) Player A plays Tops and Player B plays right

d) Player A plays Bottom and Player B plays Right

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, what will be the outcome of the game?

a)player A plays Tops and Player B plays left

b) Player A plays Bottom and Player B plays Left

c) Player A plays Tops and Player B plays Left

d) Player A plays Bottom and Player B plays Right