Cournot Oligopoly and Concavo-Concave Demand
The N-firm Cournot model with general technologies is reviewed to derive generalized and unified conditions for existence of a pure strategy Nash equilibrium. Tight conditions are formulated alternatively (i) in terms of concavity of two-sided transforms of inverse demand, or (ii) as linear constraints on the elasticities of inverse demand and its first derivative. These conditions hold, in particular, if a firm’s marginal revenue decreases in other firms’ aggregate output, or if inverse demand is logconcave. The analysis relies on lattice-theoretic methods, engaging both cardinal and ordinal notions of supermodularity. As a byproduct, a powerful test for strict quasiconcavity is obtained.
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