Use the following game matrix for questions 9-11. Firm B C D Firm A A (50,50) (5
ID: 1160474 • Letter: U
Question
Use the following game matrix for questions 9-11.
Firm B
C D
Firm A A (50,50) (500-X, 200)
B (100, 500 - X) (50, 50)
For what values of x is strategy D strictly dominant for Firm B?
Select one:
a. All x > 450.
b. All x < 450.
c. x = 450.
d. x < 50.
For what values of x is strategy B strictly dominant for Firm A?
Select one:
a. All x > 450.
b. All x < 450.
c. x = 450.
d. x < 50.
For what values of x is strategy (B, D) the only Nash equilibrium of the game?
Select one:
a. All x > 450.
b. All x < 450.
c. x = 450.
d. x < 50.
Explanation / Answer
1. a. All x > 450
Strategy D will be the dominant strategy of Firm B when it gives firm higher payoff irrespective of decision of other firm. When firm A chooses strategy A then payoff of firm B is higher when it chooses D as 200 is greater than 50. When Firm A chooses strategy B then payoff of firm B is uncertain and to make it certain payoff of D must be greater than payoff under strategy C. This implies 500 - X > 50 i.e. X > 450.
2. a. All x > 450
Strategy B will be the dominant strategy of Firm A when it gives firm higher payoff irrespective of decision of other firm. When firm B chooses strategy C then payoff of firm A is higher when it chooses B as 100 is greater than 50. When Firm B chooses strategy D then payoff of firm A is uncertain and to make it certain payoff of strategy A must be greater than payoff under strategy B. This implies 500 - X > 50 i.e. X > 450.
3. a. All x > 450
When dominant strategy of player A is to choose strategy B and player B has dominant strategy of choosing D then nash equilibrium of the game will be (B, D). This means x > 450.
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