Collusion
Assume a market with demand curve Q = 1000 -10P. There are two firms competing in the market, with constant and identical marginal costs of production of £30. They compete on the basis of quantity.
a) Find the Nash equilibrium quantities, prices and profits of the Cournot game.
b) Solve for quantities, prices and profits under the collusive outcome.
c) Solve for quantities, prices and profits when one firm produces the collusive output and the other deviates (or cheats).
d) Explain why the firms face a prisoners' dilemma.
Assume that the game is repeated infinitely and that each firm has a discount factor, δ = 0.5.
e) Is collusion sustained if each firm assumes that their competitor will follow the Grim Trigger Strategy?
f) Consider a 'stick-and-carrot' strategy whereby each firm promises to punish deviation by producing an output of 500 units in the following period, but will subsequently revert to the collusive output.
i. Is collusion sustained under, this strategy?
ii. Is such a strategy credible?
g) What implications do your results have for competition policy?