Consider an infinitely repeated Cournot competition with N firms. The market demand is Q(p) = 14 – p. All firms have the same cost function TC(q) = 2q. The common discount factor of firms is δ < 1. Suppose all your opponents play the grim strategy. Compute the lowest value of δ for which your best response is to play the grim strategy yourself.
Grim strategy: In the first period, set q = qM/N, where qM is the monopoly quantity. In each subsequent period, set q = qM/N if all firms have set q = qM/N in all past periods, otherwise set q = qCRN. (qCRN is the Cournot-Nash equilibrium quantity without repetition.)