-Consider the oil-drilling game depicted in Figure 5.4 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 round is 15 percent. At what discount rate are the players indifferent between cooperating and defecting?
A) 20 percent.
B) 27.5 percent.
C) 32.75 percent.
D) 45 percent.
E) None of the above.

Question

-Consider the oil-drilling game depicted in Figure 5.4 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 round is 15 percent. At what discount rate are the players indifferent between cooperating and defecting?
A) 20 percent. 
B) 27.5 percent. 
C) 32.75 percent. 
D) 45 percent. 
E) None of the above.

Quizplus · Accepted Answer

In repeated games, the discount rate affects players' preferences between immediate and future payoffs. When players are indifferent between cooperating and defecting, the expected payoff from cooperating equals the expected payoff from defecting, adjusted for the probability of the game continuing and the discount rate. Given a 15% chance of the game ending each round, there's an 85% chance of it continuing. The discount rate that makes players indifferent can be found by setting the expected payoffs equal and solving for the discount rate, which in this case is 27.5%. This calculation involves understanding the relationship between the continuation probability, the discount rate, and how they influence players' strategies in repeated games.

-Consider the Oil-Drilling Game Depicted in Figure 5