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, \,\delta
, 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 \,\delta
has to satisfy in order for the collusion to be sustained in both states?
ii) if \,\delta
=1/2 what is the price in state 2 (high demand) which can be sustained in equilibrium and gives the highest intertemporal profit?