UNSPECIFIED (2000) Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices. JOURNAL OF MATHEMATICAL ECONOMICS, 34 (1). pp. 39-53. ISSN 0304-4068

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Abstract

In this paper, we analyse a model of non-cooperative exchange "a la Cournot-Nash", proposed by Lloyd S. Shapley, in limit exchange economies. In contrast with the case with a finite number of traders, analysed by Sahi and Yao [Sahi, S., Yao, S., 1989, The non-cooperative equilibria of a trading economy with complete markets and consistent prices, Journal of Mathematical Economics 18, 325-346], we show that the non-uniqueness of market clearing prices induces an indeterminacy in traders' payoffs for individual deviations. In order to overcome this difficulty, we define a Cournot-Nash equilibrium concept by considering as possible equilibria only the strategy selections for which the aggregate bid matrix is irreducible. Then, we show an equivalence "a la Aumann" between the set of Cournot-Nash equilibrium allocations and the set of Walras equilibrium allocations under the assumption that the set of commodities in the economy is a net. Finally, we show the existence of a Cournot-Nash equilibrium as an easy corollary of the equivalence theorem. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C72; D51.

Item Type:	Journal Article
Subjects:	H Social Sciences > HC Economic History and Conditions Q Science > QA Mathematics H Social Sciences
Journal or Publication Title:	JOURNAL OF MATHEMATICAL ECONOMICS
Publisher:	ELSEVIER SCIENCE SA
ISSN:	0304-4068
Date:	August 2000
Volume:	34
Number:	1
Number of Pages:	15
Page Range:	pp. 39-53
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13236

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