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Unique equilibrium in contests with incomplete information

Author

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  • Christian Ewerhart
  • Federico Quartieri
Abstract
Considered are imperfectly discriminating contests in which players may possess private information about the primitives of the game, such as the contest technology, valuations of the prize, cost functions, and budget constraints. We find general conditions under which a given contest of incomplete information admits a unique pure-strategy Nash equilibrium. In particular, provided that all players have positive budgets in all states of the world, existence requires only the usual concavity and convexity assumptions. Information structures that satisfy our conditions for uniqueness include independent private valuations, correlated private values, pure common values, and examples of interdependent valuations. The results allow dealing with inactive types, asymmetric equilibria, population uncertainty, and the possibility of resale. It is also shown that any player that is active with positive probability ends up with a positive net rent.

Suggested Citation

  • Christian Ewerhart & Federico Quartieri, 2013. "Unique equilibrium in contests with incomplete information," ECON - Working Papers 133, Department of Economics - University of Zurich, revised Nov 2018.
    • Handle: RePEc:zur:econwp:133
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    Cited by:

    1. Zenou, Yves & Xu, Jin & Zhou, Junjie, 2019. "Networks in Conflict: A Variational Inequality Approach," CEPR Discussion Papers 13647, C.E.P.R. Discussion Papers.
    2. Sérgio O. Parreiras & Anna Rubinchik, 2020. "Ex ante heterogeneity in all-pay many-player auctions with Pareto distribution of costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 765-783, October.
    3. Ezra Einy & Diego Moreno & Benyamin Shitovitz, 2017. "The value of public information in common-value Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 925-942, April.
    4. 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).
    5. Edith Elkind & Abheek Ghosh & Paul W. Goldberg, 2024. "Continuous-Time Best-Response and Related Dynamics in Tullock Contests with Convex Costs," Papers 2402.08541, arXiv.org, revised Oct 2024.
    6. Ben Chen & José A. Rodrigues-Neto, 2023. "The interaction of emotions and cost-shifting rules in civil litigation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 841-885, April.
    7. Sakshi Gupta & Ram Singh, 2018. "On Existence and Properties of Pure-strategy Equilibria under Contests," Working papers 288, Centre for Development Economics, Delhi School of Economics.
    8. Qiang Fu & Jingfeng Lu & Yue Pan, 2015. "Team Contests with Multiple Pairwise Battles," American Economic Review, American Economic Association, vol. 105(7), pages 2120-2140, July.
    9. Ori Haimanko, 2022. "Equilibrium existence in two-player contests without absolute continuity of information," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 27-39, May.
    10. Ezra Einy & Diego Moreno & Aner Sela, 2020. "Continuity and robustness of Bayesian equilibria in Tullock contests," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 333-345, October.
    11. Christian Ewerhart & Julia Lareida, 2018. "Voluntary disclosure in asymmetric contests," ECON - Working Papers 279, Department of Economics - University of Zurich, revised Jul 2023.
    12. Ezra Einy & Ori Haimanko & David Lagziel, 2022. "Strong robustness to incomplete information and the uniqueness of a correlated equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 91-119, February.
    13. Eliaz, Kfir & Wu, Qinggong, 2018. "A simple model of competition between teams," Journal of Economic Theory, Elsevier, vol. 176(C), pages 372-392.
    14. Rene Kirkegaard, 2023. "Financial Constraints and Multivariate Incomplete Information in the Mixture Model of Contests," Working Papers 2402, University of Guelph, Department of Economics and Finance.
    15. Marco Serena, 2017. "Harnessing Beliefs to Stimulate Efforts; on the Optimal Disclosure Policy in Contests," Working Papers tax-mpg-rps-2018-11, Max Planck Institute for Tax Law and Public Finance.
    16. Aner Sela & Ishay Rabi & Chen Cohen, 2024. "Reputation in Contests," Working Papers 2409, Ben-Gurion University of the Negev, Department of Economics.
    17. Xu, Jin & Zenou, Yves & Zhou, Junjie, 2022. "Equilibrium characterization and shock propagation in conflict networks," Journal of Economic Theory, Elsevier, vol. 206(C).
    18. 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.
    19. Aner Sela & Ishay Rabi & Chen Cohen, 2023. "An Algorithmic Analysis of Parallel Contests," Working Papers 2317, Ben-Gurion University of the Negev, Department of Economics.
    20. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    21. Ori Haimanko, 2021. "Bayesian Nash equilibrium existence in (almost continuous) contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1231-1258, April.

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    More about this item

    Keywords

    Imperfectly discriminating contests; private information; existence and uniqueness of equilibrium; budget constraints; rent dissipation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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