Consider a situation where two firms, 1 and 2, compete by choosing prices simultaneously. They can either compete (charge a low price) or cooperate (collude, charging a high price). The firms play this competition game repeatedly and indefinitely, using a grim trigger strategy to incentivize cooperation. They use the same interest rate, i, to discount future payoffs. Payoffs are $4,050 when both firms cooperate and $3,600 when they compete. If one firm charge a low price while the other charges a high price, the firm charging the low price gets $7,200, and the other gets zero, but now assume there is a 10% chance that a regulatory agency will give both firms a $1,500 fine in each period if they are caught colluding. Find the condition on the interest rate, i , necessary for sustaining the cooperative equilibrium. Which of the following statements is correct? (a) For any i < 1/7 the firms will cooperate. (b) For any i < 1/11 the firms will cooperate. (c) For any i > 1/11 the firms will cooperate. (d) For i = 1/7 the firms will be indifferent between cooperating or competing.
Consider a situation where two firms, 1 and 2, compete by choosing prices simultaneously. They
can either compete (charge a low price) or cooperate (collude, charging a high price). The firms
play this competition game repeatedly and indefinitely, using a grim trigger strategy to
incentivize cooperation. They use the same interest rate, i, to discount future payoffs. Payoffs
are $4,050 when both firms cooperate and $3,600 when they compete. If one firm charge a low
price while the other charges a high price, the firm charging the low price gets $7,200, and the
other gets zero, but now assume there is a 10% chance that a
regulatory agency will give both firms a $1,500 fine in each period if they are caught colluding.
Find the condition on the interest rate, i , necessary for sustaining the cooperative equilibrium.
Which of the following statements is correct?
(a) For any i < 1/7 the firms will cooperate.
(b) For any i < 1/11 the firms will cooperate.
(c) For any i > 1/11 the firms will cooperate.
(d) For i = 1/7 the firms will be indifferent between cooperating or competing.
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