Grim strategy-cournot-nash equilibrium quantity

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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.)

Reference no: EM131159521

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