Cournot Duopoly
Two firms simultaneously choose quantities q₁ and q₂ of an identical good. The market price is P = 120 − (q₁ + q₂) and production is costless. What quantity does each firm produce in the Nash equilibrium?
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Source: Antoine Augustin Cournot, 'Recherches sur les principes mathematiques de la theorie des richesses' (1838). Statement written for AxiomIQ.