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Equilibrium existence in group contests

Author

Listed:
  • Philip Brookins

    (Florida State University)

  • Dmitry Ryvkin

    (Florida State University)

Abstract

We prove the existence of pure strategy Bayesian equilibria in group contests under individual-level and group-level private information. For the latter type, we develop a novel approach reducing group contests to contests between individuals with multi-dimensional types, with far-reaching implications for the existence of equilibrium in various group contest settings, including the case of complete information.

Suggested Citation

  • Philip Brookins & Dmitry Ryvkin, 2016. "Equilibrium existence in group contests," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 265-276, October.
    • Handle: RePEc:spr:etbull:v:4:y:2016:i:2:d:10.1007_s40505-015-0085-5
    DOI: 10.1007/s40505-015-0085-5
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    References listed on IDEAS

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    1. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    2. Wasser, Cédric, 2013. "A note on Bayesian Nash equilibria in imperfectly discriminating contests," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 180-182.
    3. Christian Ewerhart, 2014. "Unique equilibrium in rent-seeking contests with a continuum of types," ECON - Working Papers 159, Department of Economics - University of Zurich.
    4. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    5. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    6. Cédric Wasser, 2013. "Incomplete information in rent-seeking contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 239-268, May.
    7. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    8. Ryvkin, Dmitry, 2010. "Contests with private costs: Beyond two players," European Journal of Political Economy, Elsevier, vol. 26(4), pages 558-567, December.
    9. Ewerhart, Christian, 2014. "Unique equilibrium in rent-seeking contests with a continuum of types," Economics Letters, Elsevier, vol. 125(1), pages 115-118.
    10. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.
    11. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    12. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    13. Mark Fey, 2008. "Rent-seeking contests with incomplete information," Public Choice, Springer, vol. 135(3), pages 225-236, June.
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    Citations

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    Cited by:

    1. Martin Kolmar & Hendrik Rommeswinkel, 2020. "Group size and group success in conflicts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 777-822, December.
    2. Christian Ewerhart & Federico Quartieri, 2020. "Unique equilibrium in contests with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 243-271, July.
    3. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    4. Boosey, Luke & Brookins, Philip & Ryvkin, Dmitry, 2019. "Contests between groups of unknown size," Games and Economic Behavior, Elsevier, vol. 113(C), pages 756-769.
    5. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    6. Luke Boosey & Philip Brookins & Dmitry Ryvkin, 2020. "Entry in group contests," Working Papers wp2020_02_01, Department of Economics, Florida State University.
    7. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    8. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2023. "On equilibrium uniqueness in generalized multi-prize nested lottery contests," Games and Economic Behavior, Elsevier, vol. 139(C), pages 180-199.
    9. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    10. Mercier, Jean-François, 2018. "Non-deterministic group contest with private information," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 47-53.

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    More about this item

    Keywords

    Group contest; Incomplete information; Equilibrium existence; Reduction;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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