Use the following to answer question:
Table 12.17
-(Table 12.17) The payoffs represent profits in millions of dollars. In this infinitely repeated game, Firm A and Firm B agree to cooperate and not offer warranty coverage. Each firm follows a grim trigger strategy. At what value of d is Firm A indifferent between keeping the agreement with Firm B and cheating on it?
A) 0.2
B) 0.4
C) 0.6
D) 0.8

Question

Use the following to answer question:
Table 12.17 
-(Table 12.17) The payoffs represent profits in millions of dollars. In this infinitely repeated game, Firm A and Firm B agree to cooperate and not offer warranty coverage. Each firm follows a grim trigger strategy. At what value of d is Firm A indifferent between keeping the agreement with Firm B and cheating on it?
A) 0.2 
B) 0.4 
C) 0.6 
D) 0.8

Quizplus · Accepted Answer

The indifference point for Firm A is the point where the profits for following the agreement and cheating are equal. In this case, if Firm A follows the agreement and Firm B detects a cheating attempt, both firms will switch to the Nash equilibrium of offering warranty coverage, resulting in profits of -2 for Firm A. If Firm A cheats and Firm B detects it, Firm A will receive profits of 1, but if Firm B does not detect it, Firm A will receive profits of 2. Therefore, the indifference point for Firm A is when:
-2 = d(1) + (1-d)(2)
Solving for d, we get:
d = 0.4
Therefore, Firm A is indifferent between keeping the agreement and cheating at a detection probability of 0.4.

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