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On the Frequency of Interior Cournot-Nash Equilibria in a Public Good Economy

Author

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  • Wolfgang Buchholz
  • Richard Cornes
  • Wolfgang Peters

Abstract

In a public good economy the distribution of initial income is an important determinant of how many individuals contribute to the public good. For the case when all individuals have identical preferences in this paper a simple formula is derived that describes the proportion of all income distributions for which an interior Cournot-Nash equilibrium will result in which every agent makes a strictly positive contribution to the public good. This formula is then applied to a standard Cobb-Douglas utility function showing that the likelihood of interior Cournot-Nash equilibria falls dramatically when the number of individuals is increased. The implications this result might have for the significance of Shibata-Warr neutrality are finally discussed.

Suggested Citation

  • Wolfgang Buchholz & Richard Cornes & Wolfgang Peters, 2003. "On the Frequency of Interior Cournot-Nash Equilibria in a Public Good Economy," CESifo Working Paper Series 982, CESifo.
    • Handle: RePEc:ces:ceswps:_982
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    References listed on IDEAS

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    1. Shibata, Hirofumi, 1971. "A Bargaining Model of the Pure Theory of Public Expenditure," Journal of Political Economy, University of Chicago Press, vol. 79(1), pages 1-29, Jan.-Feb..
    2. Cornes,Richard & Sandler,Todd, 1996. "The Theory of Externalities, Public Goods, and Club Goods," Cambridge Books, Cambridge University Press, number 9780521477185, October.
    3. Warr, Peter G., 1983. "The private provision of a public good is independent of the distribution of income," Economics Letters, Elsevier, vol. 13(2-3), pages 207-211.
    4. Richard Cornes & Roger Hartley, 2007. "Aggregative Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 201-219, April.
    5. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    6. Andreoni, James, 1988. "Privately provided public goods in a large economy: The limits of altruism," Journal of Public Economics, Elsevier, vol. 35(1), pages 57-73, February.
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    Cited by:

    1. Joaquim Silvestre, 2012. "All but one free ride when wealth effects are small," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 201-207, March.
    2. Pierre Salmon, 2003. "The assignment of powers in an open-ended European Union," Post-Print hal-00445601, HAL.
    3. Buchholz, Wolfgang & Cornes, Richard & Rübbelke, Dirk, 2011. "Interior matching equilibria in a public good economy: An aggregative game approach," Journal of Public Economics, Elsevier, vol. 95(7-8), pages 639-645, August.
    4. Wolfgang Buchholz & Richard Cornes & Dirk T. G. Rübbelke, 2009. "Existence and Warr Neutrality for Matching Equilibria in a Public Good Economy: An Aggregative Game Approach," CESifo Working Paper Series 2884, CESifo.

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    More about this item

    Keywords

    private provision of public goods; Cournot-Nash equilibria; Shibata-Warr neutrality;
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