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Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium

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  • PAUL ROTHSTEIN

Abstract

We define a class of games with discontinuous payoffs that we call shared resource games and establish a pure strategy Nash equilibrium existence theorem for these games. We then apply this result to a canonical game of fiscal competition for mobile capital. Other applications are also discussed. Our result for the mobile capital game holds for any finite number of regions, permits general preferences over private and public goods, and does not assume that production technologies have a particular functional form, or are identical in all regions, or satisfy the Inada condition at zero.

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  • Paul Rothstein, 2007. "Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 335-368, April.
    • Handle: RePEc:bla:jpbect:v:9:y:2007:i:2:p:335-368
    DOI: 10.1111/j.1467-9779.2007.00310.x
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    1. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, November.
    2. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, November.
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    Cited by:

    1. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Post-Print hal-01396183, HAL.
    2. Taugourdeau, Emmanuelle & Ziad, Abderrahmane, 2011. "On the existence of Nash equilibria in an asymmetric tax competition game," Regional Science and Urban Economics, Elsevier, vol. 41(5), pages 439-445, September.
    3. Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
    4. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    5. Gaigné, Carl & Riou, Stéphane & Thisse, Jacques-François, 2016. "How to make the metropolitan area work? Neither big government, nor laissez-faire," Journal of Public Economics, Elsevier, vol. 134(C), pages 100-113.
    6. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," PSE-Ecole d'économie de Paris (Postprint) hal-01396183, HAL.
    7. Guillaume Cheikbossian, 2016. "The political economy of (De)centralization with complementary public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 315-348, August.
    8. Amrita Dhillon & Myrna Wooders & Ben Zissimos, 2007. "Tax Competition Reconsidered," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(3), pages 391-423, June.
    9. Kempf, Hubert & Rota-Graziosi, Grégoire, 2010. "Endogenizing leadership in tax competition," Journal of Public Economics, Elsevier, vol. 94(9-10), pages 768-776, October.
    10. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
    11. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    12. Hubert Kempf & Grégoire Rota-Graziosi, 2010. "Endogenizing leadership in the tax competition race," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00492105, HAL.
    13. Emmanuelle Taugourdeau & Abderrahmane Ziad, 2010. "Further Consideration of the Existence of Nash Equilibria in an Asymmetric Tax Competition Game," Post-Print halshs-00492098, HAL.
    14. Grégoire ROTA-GRAZIOSI & Hubert KEMPF, 2009. "Leading and losing the tax competition race," Working Papers 200921, CERDI.
    15. Zissimos, Ben & Wooders, Myrna, 2005. "Relaxing Tax Competition through Public Good Differentiation," Economic Research Papers 269630, University of Warwick - Department of Economics.
    16. Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01071678, HAL.
    17. Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Working Papers hal-01071678, HAL.
    18. Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
    19. Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.

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