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Nash equilibrium existence and uniqueness in a club model

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  • Fraser, Clive D.

Abstract

We model a single-club-heterogeneous-consumer-exogeneous-income economy as an aggregative public good game. Under common assumptions, if club quality functions are homogeneous of positive degree in the club facility investment and use, an unique Nash equilibrium exists.

Suggested Citation

  • Fraser, Clive D., 2012. "Nash equilibrium existence and uniqueness in a club model," Economics Letters, Elsevier, vol. 117(2), pages 496-499.
    • Handle: RePEc:eee:ecolet:v:117:y:2012:i:2:p:496-499
    DOI: 10.1016/j.econlet.2012.06.047
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    References listed on IDEAS

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    1. Andreoni, James & Bergstrom, Ted, 1996. "Do Government Subsidies Increase the Private Supply of Public Goods?," Public Choice, Springer, vol. 88(3-4), pages 295-308, September.
    2. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    3. Kotchen, Matthew J., 2007. "Equilibrium existence and uniqueness in impure public good models," Economics Letters, Elsevier, vol. 97(2), pages 91-96, November.
    4. Bergstrom, Ted C. & Blume, Larry & Varian, Hal, 1992. "Uniqueness of Nash equilibrium in private provision of public goods : An improved proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 391-392, December.
    5. Berglas, Eitan & Helpman, Elhanan & Pines, David, 1982. "The economic theory of clubs : Some clarifications," Economics Letters, Elsevier, vol. 10(3-4), pages 343-348.
    6. Fraser, Clive D., 2005. "Corrigendum to "When is efficiency separable from distribution in the provision of club goods?" [Journal of Economic Theory 90 (2000) 204-221]," Journal of Economic Theory, Elsevier, vol. 125(2), pages 194-197, December.
    7. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    8. 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.
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    10. Nett, Lorenz & Peters, Wolfgang, 1993. "The uniqueness of the subscription equilibrium with endogenous labor supply," Economics Letters, Elsevier, vol. 42(2-3), pages 139-142.
    11. Andreoni, James, 1990. "Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving?," Economic Journal, Royal Economic Society, vol. 100(401), pages 464-477, June.
    12. Hideo Konishi, 2010. "Efficient Mixed Clubs: Nonlinear‐Pricing Equilibria With Entrepreneurial Managers," The Japanese Economic Review, Japanese Economic Association, vol. 61(1), pages 35-63, March.
    13. Fraser, Clive D., 1992. "The uniqueness of Nash equilibrium in the private provision of public goods : An alternative proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 389-390, December.
    14. Cornes, Richard & Sandler, Todd, 1984. "Easy Riders, Joint Production, and Public Goods," Economic Journal, Royal Economic Society, vol. 94(375), pages 580-598, September.
    15. Cornes, Richard & Sandler, Todd, 1994. "The comparative static properties of the impure public good model," Journal of Public Economics, Elsevier, vol. 54(3), pages 403-421, July.
    16. Fraser, Clive D., 2000. "When Is Efficiency Separable from Distribution in the Provision of Club Goods?," Journal of Economic Theory, Elsevier, vol. 90(2), pages 204-221, February.
    17. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
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    Cited by:

    1. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
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    3. Klis Anna A., 2019. "On the Openness of Unique Pure-Strategy Nash Equilibrium," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(1), pages 1-9, January.

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    More about this item

    Keywords

    Nash equilibrium; Heterogeneous clubs; Aggregative game; Homogeneous functions; Existence and uniqueness;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D1 - Microeconomics - - Household Behavior
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • H4 - Public Economics - - Publicly Provided Goods

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