How does the minimum discount factor depend on the number of firms?

Suppose that demand is given by P = A − Q and marginal costs are constant and equal to c where A > c. Suppose that there are n firms and the stage game is Cournot.

(a) Find the critical value of the discount factor to sustain collusion if the firms play a super game and use grim punishment strategies. Assume that the collusive agreement involves equal sharing of monopoly output and profits.

(b) How does the minimum discount factor depend on the number of firms? Why?