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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Paper provided by Institute for Empirical Research in Economics - IEW in its series IEW - Working Papers with number
iewwp427.
Find related papers by JEL classification: L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
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