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Strategic Interactions and Atoms’ Power in Public Goods Economies*

Published online by Cambridge University Press:  09 January 2015

Hovav Perets  and
Benyamin Shitovitz
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Summary

In this paper we study the Nash equilibrium in a smooth public goods economy, described as a non-cooperative game, where the set of players is a mixed measure space of consumers. We assume a finite number of private goods. We show that under certain conditions there exists a unique Nash equilibrium in the economy, where the public goods are produced with a linear technology. Moreover, we discuss the difference in market power between an atomless sector and an atom with the same utility function, and an atom with its split atomless sector, both in a pure exchange economy and a public goods economy.

Dans cet article, nous étudions l'équilibre de Nash dans une économie d'échange avec biens publics. Cette économie décrit un jeu avec un espace mesuré mixte d'agents. Il est supposé un nombre fini de biens privés. Nous montrons qu'il existe, sous certaines conditions, un unique équilibre de Nash pour cette économie dans laquelle les biens publics sont produits avec une technologie linéaire. De plus, nous discutons de la différence en termes de pouvoir de marché qu'il existe entre une situation dans laquelle le secteur non atomique et un atome ont la même fonction d'utilité, et une situation où l'atome devient négligeable.

Keywords

public goodsprivate provision of public goodsNash equilibriummixed measure space of consumerslinear technologyC72H41biens publicsfourniture privée de biens publicséquilibre de Nashespace mesuré mixte d'agentstechnologie linéaireC72H41
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 79 , Issue 4 , December 2013 , pp. 33 - 44
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 2013 

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Footnotes

*

Part of this work is based on Perets’ Ph.D. thesis (2010) supervised by Prof. Shitovitz, University of Haifa, Israel. An earlier versions on the subject had been presented by both authors in workshops (2011 and 2012) on “Strategic Interactions and General Equilibrium: Theories and Applications II and III”, Universities Nanterre and Bourgogne, France.

We are grateful to Associate Editor and two anonymous referees for their helpful comments and suggestions. Of course, all remaining errors are ours.

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