Table 1217 The payoffs represent profits in millions of doll

(Table 12.17) The payoffs represent profits in millions of dollars.

In this infinitely repeated game, Firm A and Firm B agree to cooperate and not offer warranty coverage. Each firm follows a grim trigger strategy. At what value of d is Firm A indifferent between keeping the agreement with Firm B and cheating on it?

Solution

If Firm A and Firm B collusively choose no warranty then Firm A will earn payoff 8 infinitely.

Now if Firm A cheates and choose Warranty then he will earn payoff of 10 for one period and then due to grim trigger strategy they will play warranty hence payoff of 5 infinitely afterwards.

To be indifferent the payoff from both strategies should be same

8+d×8+d^2×8+....=10+5+5×d+5×d^2+...

8/(1-d)=10+5/(1-d)

3/(1-d)=10

d=0.7

For this value of d firm A will be indifferent

But i don\'t see any of the option matching with correct option

Kindly reconfirm the options and follow the same process given