Consider two identical firms with constant marginal costs c1 = c2 = c, and no capacity
constraints, who both discount future payoffs with the discount factor ζ. They interact repeatedly in the same market, using Cournot competition. Demand is given by P(Q) = 1 - 2Q,
where Q = q1 + q2
1. Suppose the two firms successfully sustain a collusive game where each sets quantity so that price is at the monopoly level in every period and they share the monopoly profits equally. This strategy continues forever. Calculate each firm's total discounted profits.
2. Now suppose that one firm deviates in a single period. What is the deviating firm's
choice of quantity and what is its profit in that period?
3. Assume that firms follow a "trigger strategy" profile: if someone has deviated, all firms set static Cournot quantities forever. Show that collusion is sustainable provided firms are patient enough, i.e. if ζ is high enough (please provide the value of the "critical discount factor" ζ∗.