There are N firms in the market with identical and constant marginal costs. Output is homogeneous. Assume the firms play a supergame with Bertrand as the stage game.
(a) Why is reversion to the Bertrand equilibrium the most severe credible punishment?
(b) Derive the condition similar to (10.7) for the critical value of the discount factor.
(c) Show that in the symmetric case, the condition for grim punishment strategies to support symmetric joint profit maximization is N(1 - δ) ≤ 1.
(d) Does the possibility of collusion depend on collusive profits? What happens to Stigler's trade off between sustainability and the extent of collusion? Why?
(e) For what values of the discount factor would reversion to Bertrand for only two periods sustain a collusive agreement to share equally the monopoly output?
(f) For any discount factor how many periods of Bertrand reversion are required to sustain a collusive agreement to share equally the monopoly output?