IDEAS home Printed from https://ideas.repec.org/a/bla/metroe/v73y2022i2p567-582.html
   My bibliography  Save this article

Existence, uniqueness, and comparative statics of Nash equilibrium in a game of voluntary public good provision with two public goods

Author

Listed:
  • Kenichi Suzuki
  • Tatsuyoshi Miyakoshi
  • Jun‐ichi Itaya
  • Akitomo Yamanashi

Abstract

This paper shows the uniqueness of a Nash equilibrium in the presence of many heterogeneous players with two public goods under Cobb–Douglas preferences. It provides a sufficient condition for a unique equilibrium including contributors providing both public goods, and shows that contributors providing both public goods appear frequently. This uniqueness property allows us to conduct a comparative statics analysis with a contributor and a free rider of both public goods, showing the role of the contributor providing both public goods.

Suggested Citation

  • Kenichi Suzuki & Tatsuyoshi Miyakoshi & Jun‐ichi Itaya & Akitomo Yamanashi, 2022. "Existence, uniqueness, and comparative statics of Nash equilibrium in a game of voluntary public good provision with two public goods," Metroeconomica, Wiley Blackwell, vol. 73(2), pages 567-582, May.
    • Handle: RePEc:bla:metroe:v:73:y:2022:i:2:p:567-582
    DOI: 10.1111/meca.12375
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/meca.12375
    Download Restriction: no
    File URL: https://libkey.io/10.1111/meca.12375?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ihori, Toshihiro, 1996. "International public goods and contribution productivity differentials," Journal of Public Economics, Elsevier, vol. 61(1), pages 139-154, July.
    2. Marta Faias & Emma Moreno‐García & Gareth D. Myles, 2020. "Bergstrom, Blume, and Varian: Voluntary contributions and neutrality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(2), pages 285-301, April.
    3. 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.
    4. Skaperdas, Stergios, 1992. "Cooperation, Conflict, and Power in the Absence of Property Rights," American Economic Review, American Economic Association, vol. 82(4), pages 720-739, September.
    5. 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.
    6. Kung, Fan-chin, 2008. "Voluntary contributions to multiple public goods in a production economy with widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1364-1378, December.
    7. Tatsuyoshi Miyakoshi & Kenichi Suzuki, 2014. "Who are the members of the international club?," Applied Economics, Taylor & Francis Journals, vol. 46(14), pages 1582-1585, May.
    8. 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.
    9. Ehlers, Lars, 2002. "Multiple public goods and lexicographic preferences: replacement principle," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 1-15, February.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Martin McGuire, 1974. "Group size, group homo-geneity, and the aggregate provision of a pure public good under cournot behavior," Public Choice, Springer, vol. 18(1), pages 107-126, June.
    15. 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.
    16. Mani, Anandi & Mukand, Sharun, 2007. "Democracy, visibility and public good provision," Journal of Development Economics, Elsevier, vol. 83(2), pages 506-529, July.
    17. John Chamberlin, 1976. "A diagrammatic exposition of the logic of collection action," Public Choice, Springer, vol. 26(1), pages 59-74, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anja Brumme & Wolfgang Buchholz & Dirk Rübbelke, 2023. "The purity of impure public goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(3), pages 493-514, June.
    2. 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.
    3. TOSHIHIRO IHORI & MARTIN C. McGUIRE, 2007. "Collective Risk Control and Group Security: The Unexpected Consequences of Differential Risk Aversion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 231-263, April.
    4. Tatsuyoshi Miyakoshi & Laixun Zhao, 2012. "Multi-National Public Goods Provision under Multilateral Income Transfers & Productivity Differences," Discussion Paper Series DP2012-19, Research Institute for Economics & Business Administration, Kobe University.
    5. Fraser, Clive D., 2012. "Nash equilibrium existence and uniqueness in a club model," Economics Letters, Elsevier, vol. 117(2), pages 496-499.
    6. Wolfgang Buchholz & Wolfgang Peters, 2001. "The overprovision anomaly of private public good supply," Journal of Economics, Springer, vol. 74(1), pages 63-78, February.
    7. Cornes, Richard & Hartley, Roger, 2007. "Weak links, good shots and other public good games: Building on BBV," Journal of Public Economics, Elsevier, vol. 91(9), pages 1684-1707, September.
    8. Morath, Florian, 2010. "Strategic information acquisition and the mitigation of global warming," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 206-217, March.
    9. 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.
    10. Buchholz, Wolfgang & Nett, Lorenz & Peters, Wolfgang, 1998. "The strategic advantage of being less skilled," Economics Letters, Elsevier, vol. 60(1), pages 35-39, July.
    11. Nicola Acocella & Giovanni Di Bartolomeo, 2010. "Conflict of interest and coordination in public good provision," Politica economica, Società editrice il Mulino, issue 3, pages 389-408.
    12. Simon Vicary, 2009. "The voluntary provision of a public good in an international commons," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 42(3), pages 984-996, August.
    13. Wolfgang Buchholz & Richard Cornes & Dirk Rübbelke, 2018. "Public goods and public bads," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(4), pages 525-540, August.
    14. Gaube, Thomas, 2000. "Group size and free riding when private and public goods are gross substitutes," Bonn Econ Discussion Papers 13/2000, University of Bonn, Bonn Graduate School of Economics (BGSE).
    15. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    16. Clive Fraser, 2012. "Milton Friedman, the Demand for Money and the ECB’s Monetary-Policy Strategy," Discussion Papers in Economics 12/06, Division of Economics, School of Business, University of Leicester.
    17. Buchholz, Wolfgang & Konrad, Kai A., 1995. "Strategic transfers and private provision of public goods," Journal of Public Economics, Elsevier, vol. 57(3), pages 489-505, July.
    18. Simon Vicary, 2009. "The voluntary provision of a public good in an international commons," Canadian Journal of Economics, Canadian Economics Association, vol. 42(3), pages 984-996, August.
    19. Tatsuyoshi Miyakoshi & Kenichi Suzuki, 2011. "The existence and uniqueness of equilibrium in the international public good model," Applied Economics Letters, Taylor & Francis Journals, vol. 18(18), pages 1751-1754, December.
    20. Wolfgang Buchholz & Todd Sandler, 2016. "The Exploitation Hypothesis in a Public Good Economy: Some Extensions," CESifo Working Paper Series 5717, CESifo.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:metroe:v:73:y:2022:i:2:p:567-582. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0026-1386 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.