Suppose the game is infinitely repeated, and the interest rate is 5%.Both firms agree to charge a high price, provided no player has charged in low price in the past.If both firms stick to this agreement, then the present value of Firm B's payoffs are:
A)105.
B)190.
C)210.
D)525.

Question

Quizplus · Accepted Answer

In an infinitely repeated game, the present value of a player's payoffs is calculated by dividing the payoff by (1+r), where r is the discount rate (interest rate). The payoffs for Firm B in this case are as follows:
- If both firms charge high, Firm B earns 100 in each period.
- If both firms charge low, Firm B earns 80 in each period.
Since there is no discounting factor for the first period, the present value of the payoffs for the subsequent periods can be calculated as follows:
PV(B-high) = 100 + (100/1.05) + (100/1.05^2) + ... = 100(1 + 1/1.05 + 1/1.05^2 + ...) = 100(1/(1-1/1.05)) = 210.52
PV(B-low) = 80 + (80/1.05) + (80/1.05^2) + ... = 80(1 + 1/1.05 + 1/1.05^2 + ...) = 80(1/(1-1/1.05)) = 168.42
Therefore, the maximum present value of Firm B's payoffs is achieved if both firms charge high, and the answer is C.

Suppose the Game Is Infinitely Repeated, and the Interest Rate