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Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via Contraction

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  • Richard Cornes
  • Roger Hartley
  • Todd Sandler

Abstract

This paper presents a proof for existence and uniqueness of a Nash equilibrium of a public good model that exploits a simple contraction mapping. The proof establishes both existence and uniqueness in a single exercise that provides intuition about sufficiency. The method of proof is applied not only to the basic pure public good model but also to the impure model. In the latter model, income normality does not play the same pivotal role for existence and uniqueness. Copyright 1999 by Blackwell Publishing Inc.

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Bibliographic Info

Paper provided by Department of Economics, Keele University in its series Keele Department of Economics Discussion Papers (1995-2001) with number 99/02.

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Date of creation: 1999
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Publication status: Published in Journal of Public Economic Theory, Vol. 1, 1999, pages 499 - 509.
Handle: RePEc:kee:keeldp:99/02

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Postal: Department of Economics, University of Keele, Keele, Staffordshire, ST5 5BG - United Kingdom
Phone: +44 (0)1782 584581
Fax: +44 (0)1782 717577
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Web page: http://www.keele.ac.uk/depts/ec/cer/
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Postal: Department of Economics, Keele University, Keele, Staffordshire ST5 5BG - United Kingdom
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Web: http://www.keele.ac.uk/depts/ec/cer/pubs_kerps.htm

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Cited by:
  1. Gaube, Thomas, 2006. "Altruism and charitable giving in a fully replicated economy," Journal of Public Economics, Elsevier, vol. 90(8-9), pages 1649-1667, September.
  2. Villanacci, Antonio & Zenginobuz, E. Unal, 2006. "Subscription equilibria with public production: Existence and regularity," Research in Economics, Elsevier, vol. 60(4), pages 199-215, December.
  3. Ulrich Schmidt, 2010. "Self-Insurance and Self-Protection as Public Goods," Kiel Working Papers 1613, Kiel Institute for the World Economy.
  4. Clive Fraser, 2012. "Milton Friedman, the Demand for Money and the ECB’s Monetary-Policy Strategy," Discussion Papers in Economics 12/06, Department of Economics, University of Leicester.
  5. Thomas Gaube, 2005. "Altruism and charitable giving in a fully replicated economy," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2005_8, Max Planck Institute for Research on Collective Goods.
  6. Thomas Gaube, 1999. "Group size and free riding when private and public goods are gross substitutes," Bonn Econ Discussion Papers bgse13_2000, University of Bonn, Germany, revised May 2000.
  7. Menezes, Flavio & Quiggin, John, 2004. "Games without Rules," Risk and Sustainable Management Group Working Papers 151166, University of Queensland, School of Economics.
  8. Roy Chowdhury, Prabal, 2006. "Alliances Among Asymmetric Countries," MPRA Paper 1502, University Library of Munich, Germany.
  9. Pittel, Karen & Rübbelke, Dirk T. G., 2006. "Private provision of public goods: Incentives for donations," Munich Reprints in Economics 19352, University of Munich, Department of Economics.
  10. Christoph Luelfesmann, 2007. "Dual Provision of Public Policies in Democracy," Discussion Papers dp07-20, Department of Economics, Simon Fraser University.
  11. Acocella Nicola & Di Bartolomeo Giovanni, 2010. "Conflict of interest and coordination in public good provision," Politica economica, Società editrice il Mulino, issue 3, pages 389-408.
  12. Emanuela Randon, 2002. "L’analisi positiva dell’esternalità: rassegna della letteratura e nuovi spunti," Working Papers 58, University of Milano-Bicocca, Department of Economics, revised Jun 2002.
  13. Gaube, Thomas, 2001. "Group size and free riding when private and public goods are gross substitutes," Economics Letters, Elsevier, vol. 70(1), pages 127-132, January.
  14. Villanacci, Antonio & Zenginobuz, E.Unal, 2005. "Existence and regularity of equilibria in a general equilibrium model with private provision of a public good," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 617-636, August.

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