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 B
|
|
Player A
|
|
Left
|
Right
|
|
Top
|
2 5
|
1 4
|
|
|
Bottom
|
0 1
|
3 8
|
where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.
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?