2 Consider two firms having the opportunity to either engage in a cartel or to p

Question

2 Consider two firms having the opportunity to either engage in a cartel or to play noncooperatively. Consider the following payoff matrix. cooperative 72,47 60,60 Concooperative 54, 54 47, 72 cooperative Solve for the interest rate which ensures that cooperation is stable. Consider the following cases: a) a finite time horizon game in which firms apply Grim trigger strategies b) a finite time horizon game in which firms apply Tit for Tat strategies c) an infinite time horizon game in which firms apply Grim trigger strategies d) an infinite time horizon game in which firms apply Tit for Tat strategies

Explanation / Answer

a. Grim trigger strategy is one in which once default leads to default always.

And in finite game firm will default to gain because there is finite numbers of game. So, in finite time horizon firm will be noncooperative and their payoff could be (54'54) or (72,47) or (47,72).

b. Tit for tat strategy is one in which the one firm do what other firm did for his last year. In finite horizon both tit for tat and grim trigger face same payoff. So the payoff in this case will also be (54,54) or (72,47) or (47,72).

c. In case of infinite time horizon there is a threat in grim trigger strategy because if one default single time the other will never trust his again. So in this case they both will cooperate and payoff will be (60,60) for the whole time. Let's say the time horizon is T years then their payoff in this case will be 60×T for T years.

And if one do not cooperate then his payoff will be 72 + (T-1)54 for T years.

d. In case of tit for tat strategy if one firm cooperate in this year than the other firm will do the same in next year.

There are 2 case in this strategy for long term cooperation stability

1. When one cooperate and other do not in this year.

Then the payoff of the firm who cooperate for T years will be

47 + (T-1)60

2. When both cooperate

Then the payoff for T years will be

60×T.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.