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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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  • Richard Cornes & Roger Hartley & Todd Sandler, 1999. "Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via Contraction," Keele Department of Economics Discussion Papers (1995-2001) 99/02, Department of Economics, Keele University.
  • Handle: RePEc:kee:keeldp:99/02
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    9. Karine Gobert & Michel Poitevin, 2006. "Non-commitment and savings in dynamic risk-sharing contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 357-372.
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    Cited by:

    1. 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.
    2. Flavio Menezes & John Quiggin, 2007. "Games without Rules," Theory and Decision, Springer, pages 315-347.
    3. 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.
    4. Prabal Roy Chowdhury, 2007. "Alliances Among Asymmetric Countries," Defence and Peace Economics, Taylor & Francis Journals, pages 253-263.
    5. 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.
    6. 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.
    7. Christoph Luelfesmann, 2007. "Dual Provision of Public Policies in Democracy," Discussion Papers dp07-20, Department of Economics, Simon Fraser University.
    8. Tim Lohse & Julio R. Robledo & Ulrich Schmidt, 2012. "Self‐Insurance and Self‐Protection as Public Goods," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 57-76, March.
    9. 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.
    10. 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.
    11. Karen Pittel & Dirk T.G. Rübbelke, 2004. "Private Provision of Public Goods : Incentives for Donations," CER-ETH Economics working paper series 04/34, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    12. 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.
    13. Todd Sandler & Daniel G. Arce M., 2003. "Pure Public Goods versus Commons: Benefit-Cost Duality," Land Economics, University of Wisconsin Press, vol. 79(3), pages 355-368.
    14. Thomas Gaube, 2005. "Altruism and charitable giving in a fully replicated economy," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2005_8, Max Planck Institute for Research on Collective Goods.
    15. 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.

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