-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 discount rate is 5 percent. What is the probability that the game will end if the players are indifferent between cooperating and defecting?
A) Around 1.6 percent.
B) Around 2.5 percent.
C) Around 3.7 percent.
D) Around 4.5 percent.
E) Around 5.2 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 discount rate is 5 percent. What is the probability that the game will end if the players are indifferent between cooperating and defecting?
A) Around 1.6 percent. 
B) Around 2.5 percent. 
C) Around 3.7 percent. 
D) Around 4.5 percent. 
E) Around 5.2 percent.

Quizplus · Accepted Answer

The correct answer is A because the probability that the game will end if the players are indifferent between cooperating and defecting is around 1.6 percent. This is because the discount rate is 5 percent, and the payoff to cooperation is 1 million dollars, while the payoff to defection is 2 million dollars. Therefore, the present value of the payoff to cooperation is 1 / (1 + 0.05) = 0.9524 million dollars, while the present value of the payoff to defection is 2 / (1 + 0.05) = 1.9048 million dollars. Therefore, the players are indifferent between cooperating and defecting if the payoff to cooperation is equal to the payoff to defection, which occurs when the present value of the payoff to cooperation is equal to the present value of the payoff to defection. This occurs when the discount rate is 5 percent and the payoff to cooperation is 1 million dollars.

-Consider the Pricing Game Depicted in Figure 5