-Consider the pricing game depicted in Figure 5.5 in which payoffs are in millions of dollars. Suppose that this game is played repeatedly and the probability that the game will end in the next stage is 1 percent. For what discount rate will a firm be indifferent between cooperating and defecting?
A) 2.5 percent.
B) 4.25 percent.
C) 5.6 percent.
D) 8.5 percent.
E) 10.25 percent.

Question

-Consider the pricing game depicted in Figure 5.5 in which payoffs are in millions of dollars. Suppose that this game is played repeatedly and the probability that the game will end in the next stage is 1 percent. For what discount rate will a firm be indifferent between cooperating and defecting?
A) 2.5 percent. 
B) 4.25 percent. 
C) 5.6 percent. 
D) 8.5 percent. 
E) 10.25 percent.

Quizplus · Accepted Answer

The discount rate at which a firm would be indifferent between cooperating and defecting in a repeated game is determined by comparing the present value of the stream of payoffs from cooperating versus defecting. Given that the game ends with a 1% probability in each stage, the continuation probability is 99% (or 0.99). The discount rate that makes a firm indifferent is the one that equates the expected present value of cooperating and defecting. This calculation involves solving for the discount rate in the equation that sets these two expected values equal, taking into account the probability of the game continuing and the payoffs from each strategy. The correct discount rate is found by solving this equation, which typically involves the use of the formula for the expected present value of an infinite series of payoffs, adjusted for the probability of continuation and the specific payoffs of the game. Given the information provided, the correct answer is derived from such a calculation, which is specific to the details of the game's payoffs and the continuation probability.

-Consider the Pricing Game Depicted in Figure 5