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
|
|
Player A
|
|
Left
|
Right
|
|
Top
|
2 5
|
1 4
|
|
|
Bottom
|
0 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 chooses-for example, "Player A plays Bottom and Player B plays Right")
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?