Consider the following supergame: N firms choose prices simultaneously in each period. The discount factor is per period. Suppose firms try to collude at the monopoly price with the threat of practicing price equal to marginal cost for T periods if any firm deviates. After the punishment period firms go back to the monopoly price.
a) define analytically the firms' strategies
b) derive the condition that has to hold so that no firm gains by deviating from the equilibrium strategy. Interpret the relationship between N, , and T.
c) Suppose firms observe the price practiced by other firms with a k period lag. How would this affect the possibility of collusion?
d) Consider the case where there are only 2 firms. Suppose that demand is stochastic, with i.i.d. shocks. In every period demand is high with probability 1/2 and low with probability 1/2. Firms choose prices simultaneously after observing whether demand is high or low. The demand curve is D1(p)=1-p when demand is low and D2(p)=2=p when demand is high.
i) What is the condition that has to satisfy in order for the collusion to be sustained in both states?
ii) if =1/2 what is the price in state 2 (high demand) which can be sustained in equilibrium and gives the highest intertemporal profit?