Question 1:  Collusion

Two firms produce identical products.  Market shares are determined as in the Bertrand model.  Each period over an infinite horizon, they simultaneously set prices.  Each firm has a constant marginal cost of c and no fixed costs.  Suppose the monopoly price is pm . It takes two periods to detect and respond to a rival deviation.

The firms consider the following (grim-trigger) strategies to collude:

p =〈

'(c       otherwise

1. Give two possible reasons that detecting a rival’s deviation can be difficult (so that it takes two periods rather than one).

2. Find the critical discount factor (level of patience), 6* , such that if both firms are more patient (ie 6 ≥ 6* ), then the cartel can be sustained using the above trigger strategies.

3. Suppose 6 < 6* . Are there any subgame perfect Nash equilibria to the repeated game? Explain.

Question 2:  Collusion

Two firms produce identical products.  Each period over an infinite horizon, they simultaneously set prices. Market shares are determined as in the Bertrand model. Each firm has a constant marginal cost of c and no fixed costs. Suppose the monopoly price is pm .

The firms consider the following strategies to collude. If both firms set p = pm  last period, then set p = pm  this period.  If either firm cheats by setting p  pm , then punish for 1 period by setting p = c, then return to p = pm  thereafter. More formally