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Cournot games with biconcave demand


Ewerhart, Christian (2014). Cournot games with biconcave demand. Working paper series / Department of Economics 16, University of Zurich.

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.

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:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C72, L13, C62
Uncontrolled Keywords:Cournot games, existence and uniqueness of a pure-strategy Nash equilibrium, generalized concavity, supermodularity
Language:English
Date:January 2014
Deposited On:25 Nov 2011 10:13
Last Modified:05 Apr 2016 15:08
Series Name:Working paper series / Department of Economics
Number of Pages:25
ISSN:1664-7041
Additional Information:Revised version
Official URL:http://www.econ.uzh.ch/static/wp/econwp016.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php
Permanent URL: http://doi.org/10.5167/uzh-51520

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