Cournot / Bertrand / Game theory- Question (Industrial Organization)

[IwantEintein'sBrain]

---

Hello! I'm preparing for exam in industrial organization and the question in the textbook is this:

Suppose, in a duopoly market with uncertainty, market demand is given by P = 140 - 2Q, and marginal cost equals 10 for both firms, which are Cournot competitors. The collusive agreement being considered is for each to produce half of the monopoly output.

A) What is the critical discount rate to sustain collusion using grim punishment strategies if detection of deviation requires two periods and the probability that the game is played in the next period is 0.95?

B) Suppose that the rules of the game are changed such that under the same cost and demand conditions the firms are now Bertrand competitors with unlimited capacity. What values of the discount rate can sustain cooperation?

C) Which type of competition - Bertrand or Cournot - is more likely to sustain the collusive agreement, and why?

In advance,
Thank you

 

[tkhunny]

First, one must prove that one has read at least one chapter in the book or attended at least one lecture.

In other words, please show YOUR work. We're happy to help math students who show personal effort.