Suppose the game is infinitely repeated, and the interest rate is 10%.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 A's payoffs are:
A)220.
B)110.
C)330.
D)550.

Question

Quizplus · Accepted Answer

In an infinitely repeated game, players have an incentive to cooperate and maintain a cooperative strategy because they have the opportunity to punish deviations from the strategy in future rounds. In this case, both firms have agreed to charge a high price, provided no player has charged a low price in the past.

Assuming both firms cooperate and stick to this strategy, they will both receive a payoff of 110 in each round, since they both charge the high price. The present value of these payoffs can be calculated as follows:

PV = 110/(1+0.1) + 110/(1+0.1)^2 + 110/(1+0.1)^3 + ... 
PV = 110*(1/(0.1)) 
PV = 1100

However, if Firm A deviates and charges a low price, they will receive a payoff of 220 for that round (since they will capture the entire market). But, if Firm B sticks to the high price, they will receive a payoff of 0 for that round. In all subsequent rounds, both firms will charge low prices and receive a payoff of 0.

The present value of this scenario can be calculated as follows:

PV = 220 + 0.1*0 + 0.1^2*0 + 0.1^3*0 + ... 
PV = 220

Since 220 is greater than 1100/2 = 550 (which is the present value of the cooperative outcome), Firm A has an incentive to deviate and charge a low price. However, if Firm B is able to punish this deviation by also charging a low price in subsequent rounds, both firms will end up worse off in the long run. Therefore, the best choice for both firms is to stick to the cooperative outcome and charge a high price in each round.

Suppose the Game Is Infinitely Repeated, and the Interest Rate