We consider two identical firms that produce the same good. The demand for that good is the function D(p) = 1 - p where p is the unit price. Firms incur no cost.
The competition game (simultaneous pricing competition) is repeated infinitely. The discount factor is δ.
We consider the following strategy for each firm:
At period t, firm i :
(i) sets the monopoly price if firm 2 sets the monopoly price at all the previous periods.
(ii) sets a price equal to 0 otherwise
1. What is the condition on δ that ensures that setting the monopoly price at each period is an equilibrium of the dynamic game?
We introduce fluctuations in the market demand. At each period the demand is, with equal probability, either 0 or 2(1 - p).
2. What is the new condition on δ that makes collusion on the monopoly price stable?