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Cournot games with biconcave demand


Ewerhart, Christian (2014). Cournot games with biconcave demand. Games and Economic Behavior, 85:37-47.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Cournot games, existence and uniqueness of a pure-strategy Nash equilibrium, generalized concavity, supermodularity
Language:English
Date:May 2014
Deposited On:29 Jan 2014 14:02
Last Modified:14 Feb 2018 21:02
Publisher:Elsevier
ISSN:0899-8256
Additional Information:See also ECON Working Paper No. 16 (http://www.zora.uzh.ch/51520/)
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/j.geb.2014.01.001

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