Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T23:34:16.098Z Has data issue: false hasContentIssue false
  • English
  • Français

Strategic Interactions and Atoms’ Power in Public Goods Economies*

Published online by Cambridge University Press:  09 January 2015

Hovav Perets  and
Benyamin Shitovitz
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Artstein, Z., 1979. A Note on Fatou's Lemma in Several Dimensions. Journal of Mathematical Economics 6, 277–282.Google Scholar
Aumann, R.J., 1964. Markets with a Continuum of Traders. Econometrica 32, 39–50.Google Scholar
Bergstrom, T., Blume, C. and Varian, H., 1986. On the Private Provision of Public Good. Journal of Public Economics 29, 25–49.Google Scholar
Bernheim, B.D., 1986. On the Voluntary and Involuntary Provision of Public Goods. American Economic Review 76, 789–793.Google Scholar
Debreu, G., 1972. Smooth Preferences. Econometrica 40, 603–615.Google Scholar
Gabszewicz, J. and Mertens, J.F. 1971. An Equivalence Theorem for the Core of an Economy Whose Atoms are not ‘Too’ Big. Econometrica 39, 713–722.Google Scholar
Gabszewicz, J. J. and Shitovitz, B., 1992. The Core in Imperfectly Competitive Economies, in: Aumann, R.J. & Hart, S. (ed.), Handbook of Game Theory with Economic Applications, Vol. I, Chapter 15, pages 459–483 Elsevier.Google Scholar
Perets, H., 2011. On Nash Equilibria in a Public Goods Economy with a Mixed Measure Space of Consumers, Ph.D. Dissertation (in Hebrew), University of Haifa, Israel.Google Scholar
Perets, H., Shitovitz, B. and Spiegel, M., 2012. Trading Equilibrium in a Public Good Economy with Smooth Preferences and a Mixed Measure Space of Consumers. Journal of Mathematical Economics 48, 163–169.Google Scholar
Schmeidler, D., 1970. Fatou's Lemma in Several Dimensions. Proceedings of the American Mathematical Society 24, 300–306.Google Scholar
Shitovitz, B., 1973, Oligopoly in Markets with a Continuum of Traders. Econometrica 41, 467–501.Google Scholar
Shitovitz, B., Spiegel, M., 1998. Cournot-Nash and Lindahl Equilibria in Pure Public Good Economies. Journal of Economic Theory 83, 1–18.Google Scholar
Shitovitz, B. and Spiegel, M., 2001. Stable Provision Vs. Cournot-Nash Equilibria in Pure Public Good Economies. Journal of Public Economic Theory 3, 219–224.Google Scholar
Warr, Peter G., 1983. The Private Provision of a Public Good is Independent of the Distribution of Income, Economics Letters, 13 (2-3): 207–211.Google Scholar