Cournot Games with Biconcave Demand

University of Zurich Working Paper No. 16

26 Pages Posted: 16 Sep 2009 Last revised: 29 Jan 2014

Christian Ewerhart

University of Zurich - Department of Economics

Date Written: January 2014

Abstract

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either "nearly linear" or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.

Keywords: Cournot games, existence and uniqueness of a pure-strategy Nash equilibrium, generalized concavity, supermodularity

JEL Classification: C72, L13, C62

Suggested Citation

Ewerhart, Christian, Cournot Games with Biconcave Demand (January 2014). University of Zurich Working Paper No. 16. Available at SSRN: https://ssrn.com/abstract=1473768 or http://dx.doi.org/10.2139/ssrn.1473768

Christian Ewerhart (Contact Author)

University of Zurich - Department of Economics ( email )

Winterthurerstrasse 30
CH-8006 Zurich
Switzerland

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