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Existence, Uniqueness, and Algorithm for Identifying Free Riders in Multiple Public Good Games: Replacement Function Approach

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  • Ken-ichi Suzuki
  • Jun-ichi Itaya
  • Akitomo Yamanashi
  • Tatsuyoshi Miyakoshi

Abstract

This study shows the uniqueness of Nash equilibrium in the model of multiple voluntarily supplied public goods with potential contributors possessing different Cobb-Douglas preferences. This study provides a sufficient condition for uniqueness using graph theory. This sufficient condition allows us to use the replacement function approach of Cornes and Hartley (2007) not only to develop an algorithm for identifying free riders, but also to provide an alternative proof for the uniqueness of a Nash equilibrium in multiple public goods models.

Suggested Citation

  • Ken-ichi Suzuki & Jun-ichi Itaya & Akitomo Yamanashi & Tatsuyoshi Miyakoshi, 2018. "Existence, Uniqueness, and Algorithm for Identifying Free Riders in Multiple Public Good Games: Replacement Function Approach," CESifo Working Paper Series 7062, CESifo.
    • Handle: RePEc:ces:ceswps:_7062
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    References listed on IDEAS

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    1. Ratna K. Shrestha & Kwang Soo Cheong, 2007. "An Alternative Algorithm for Identifying Free Riders Based on a No-Free-Rider Nash Equilibrium," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 63(2), pages 278-284, June.
    2. Richard Cornes & Roger Hartley & Todd Sandler, 1999. "Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via Contraction," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(4), pages 499-509, October.
    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. Kemp, Murray C., 1984. "A note of the theory of international transfers," Economics Letters, Elsevier, vol. 14(2-3), pages 259-262.
    6. Cornes, Richard & Hartley, Roger, 2012. "Fully aggregative games," Economics Letters, Elsevier, vol. 116(3), pages 631-633.
    7. 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.
    8. 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.
    9. 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.
    10. Richard Cornes & Jun‐Ichi Itaya, 2010. "On the Private Provision of Two or More Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(2), pages 363-385, April.
    11. Yildirim, Huseyin, 2014. "Andreoni–McGuire algorithm and the limits of warm-glow giving," Journal of Public Economics, Elsevier, vol. 114(C), pages 101-107.
    12. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," Economics Discussion Paper Series 0514, Economics, The University of Manchester.
    13. Andreoni, James & McGuire, Martin C., 1993. "Identifying the free riders : A simple algorithm for determining who will contribute to a public good," Journal of Public Economics, Elsevier, vol. 51(3), pages 447-454, July.
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    More about this item

    Keywords

    public good; voluntary provision; uniqueness; aggregate game; Nash equilibrium; algorithm;
    All these keywords.

    JEL classification:

    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • F13 - International Economics - - Trade - - - Trade Policy; International Trade Organizations
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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