the Cournot model, economics homework help

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Consider a repeated version of the Cournot model discussed in class, with two firms i = 1, 2, demand
P (Q) = (A − Q)+ ,
marginal production production costs ci > 0 (satisfying c1, c2 < A) and discount factor ↵ 2 (0, 1).

Find out a strategy profile that induced these firms to cooperate in this market (i.e., to collude by
producing in total the monopoly quantity A

b) Now suppose firms want to sustain cooperation in an asymmetric way. Describe a strategy profile that
induces these firms to cooperate, for large enough discount factor “, in an asymmetric way, i.e., to produce
the monopoly quantity in total (which maximizes total profits in the stage game) with firm 1 producing
share ↵1 2 (0, 1) of this quantity and firm 2 producing share ↵2 2 (0, 1) of this quantity, with ↵1 + ↵2 = 1.
Suppose that ↵1 < ↵2. Find how large the discount factor ” needs to be for cooperation to be sustained
(Hint: you can use modified grim-trigger strategies for this question).

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