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

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  • Cornes, Richard
  • Hartley, Roger
  • Sandler, Todd

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 Iowa State University, Department of Economics in its series Staff General Research Papers with number 1630.

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Date of creation: 01 Oct 1999
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Publication status: Published in Journal of Public Economic Theory, October 1999, vol. 1 no. 4, pp. 499-509
Handle: RePEc:isu:genres:1630

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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Cited by:
  1. Villanacci, Antonio & Zenginobuz, E. Unal, 2006. "Subscription equilibria with public production: Existence and regularity," Research in Economics, Elsevier, Elsevier, vol. 60(4), pages 199-215, December.
  2. Roy Chowdhury, Prabal, 2006. "Alliances Among Asymmetric Countries," MPRA Paper 1502, University Library of Munich, Germany.
  3. Acocella Nicola & Di Bartolomeo Giovanni, 2010. "Conflict of interest and coordination in public good provision," Politica economica, Società editrice il Mulino, Società editrice il Mulino, issue 3, pages 389-408.
  4. Thomas Gaube, 1999. "Group size and free riding when private and public goods are gross substitutes," Bonn Econ Discussion Papers, University of Bonn, Germany bgse13_2000, University of Bonn, Germany, revised May 2000.
  5. Emanuela Randon, 2002. "L’analisi positiva dell’esternalità: rassegna della letteratura e nuovi spunti," Working Papers, University of Milano-Bicocca, Department of Economics 58, University of Milano-Bicocca, Department of Economics, revised Jun 2002.
  6. Flavio Menezes & John Quiggin, 2007. "Games without Rules," Theory and Decision, Springer, Springer, vol. 63(4), pages 315-347, December.
  7. Pittel, Karen & Rübbelke, Dirk T. G., 2006. "Private provision of public goods: Incentives for donations," Munich Reprints in Economics, University of Munich, Department of Economics 19352, University of Munich, Department of Economics.
  8. Clive Fraser, 2012. "Milton Friedman, the Demand for Money and the ECB’s Monetary-Policy Strategy," Discussion Papers in Economics, Department of Economics, University of Leicester 12/06, Department of Economics, University of Leicester.
  9. 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.
  10. Gaube, Thomas, 2006. "Altruism and charitable giving in a fully replicated economy," Journal of Public Economics, Elsevier, Elsevier, vol. 90(8-9), pages 1649-1667, September.
  11. Lohse, Tim & Julio R. Robledo & Ulrich Schmidt, 2006. "Self-Insurance and Self-Protection as Public Goods," Hannover Economic Papers (HEP), Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät dp-354, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  12. 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, Max Planck Institute for Research on Collective Goods 2005_8, Max Planck Institute for Research on Collective Goods.
  13. Gaube, Thomas, 2001. "Group size and free riding when private and public goods are gross substitutes," Economics Letters, Elsevier, Elsevier, vol. 70(1), pages 127-132, January.
  14. Christoph Luelfesmann, 2007. "Dual Provision of Public Policies in Democracy," Discussion Papers dp07-20, Department of Economics, Simon Fraser University.

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