Cournot Oligopoly and Concavo-Concave Demand
AbstractThe 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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Bibliographic InfoPaper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 427.
Date of creation: Sep 2009
Date of revision:
Cournot competition; existence of Nash equilibrium; concavity of demand; supermodular games; strict quasiconcavity;
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; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-10-03 (All new papers)
- NEP-BEC-2009-10-03 (Business Economics)
- NEP-COM-2009-10-03 (Industrial Competition)
- NEP-IND-2009-10-03 (Industrial Organization)
- NEP-MIC-2009-10-03 (Microeconomics)
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- Pierre von Mouche & Federico Quartieri, 2013. "On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility," Journal of Global Optimization, Springer, Springer, vol. 57(3), pages 707-718, November.
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