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Existence And Uniqueness Of Equilibrium In Asymmetric Contests With Endogenous Prizes

Author

Listed:
  • SHUMEI HIRAI

    (Department of Economics, Daito Bunka University, 560 Iwadono, Higashimatsuyama-shi, Saitama 355-8501, Japan)

  • FERENC SZIDAROVSZKY

    (Department of Applied Mathematics, University of Pécs, Ifjusag u.6, H-7624, Pécs, Hungary)

Abstract

This paper considers contests in which the efforts of the players determine the value of the prize. Players may have different valuations of the prize and different abilities to convert expenditures to productive efforts. In addition, players may face different financial constraints. This paper presents a proof for the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with endogenous prizes.

Suggested Citation

  • Shumei Hirai & Ferenc Szidarovszky, 2013. "Existence And Uniqueness Of Equilibrium In Asymmetric Contests With Endogenous Prizes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-9.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:01:n:s0219198913500059
    DOI: 10.1142/S0219198913500059
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    References listed on IDEAS

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    1. Bruce D. Craven & Sardar M. N. Islam, 2005. "Optimization in Economics and Finance," Dynamic Modeling and Econometrics in Economics and Finance, Springer, number 978-0-387-24280-4, May.
    2. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
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    Cited by:

    1. Damian S. Damianov & Shane Sanders & Anil Yildizparlak, 2018. "Asymmetric endogenous prize contests," Theory and Decision, Springer, vol. 85(3), pages 435-453, October.
    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. Peter Hubert Mathieu Mouche & Ferenc Szidarovszky, 2023. "Aggregative Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1056-1092, March.
    4. Akio Matsumoto & Ferenc Szidarovszky, 2022. "Stability of dynamic asymmetric contests with endogenous prizes," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 29-40, January.
    5. Nicola Gennaioli & Hans-Joachim Voth, 2015. "State Capacity and Military Conflict," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1409-1448.
    6. Betto, Maria & Thomas, Matthew W., 2024. "Asymmetric all-pay auctions with spillovers," Theoretical Economics, Econometric Society, vol. 19(1), January.
    7. Koji Okuguchi & Takeshi Yamazaki, 2018. "Existence of Unique Equilibrium in Cournot Mixed Oligopoly," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-13, September.
    8. Malin Arve & Olga Chiappinelli, 2021. "The Role of Budget Constraints in Sequential Elimination Tournaments," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(4), pages 1059-1087, October.
    9. Cheikbossian, Guillaume, 2021. "The evolutionary stability of in-group altruism in productive and destructive group contests," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 236-252.
    10. Walter Ferrarese, 2018. "Equilibrium Effort in Games with Homogeneous Production Functions and Homogeneous Valuation," CEIS Research Paper 432, Tor Vergata University, CEIS, revised 12 Nov 2021.
    11. Christian Cox, 2023. "Lobbying for government appropriations," RAND Journal of Economics, RAND Corporation, vol. 54(3), pages 443-483, September.
    12. von Mouche, Pierre & Szidarovszky, Ferenc, 2024. "Aggregative games with discontinuous payoffs at the origin," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 77-84.
    13. Masaki Fujimoto, 2023. "A Dynamic Analysis of Equal Revenue Sharing and Endogenous Salary Caps in the N-Team Leagues," Journal of Sports Economics, , vol. 24(5), pages 624-638, June.
    14. Walter Ferrarese, 2022. "Equilibrium effort in games with homogeneous production functions and homogeneous valuation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(2), pages 195-212, June.
    15. Chung, A., 2024. "Target Setting in Contests with Sabotage," Cambridge Working Papers in Economics 2409, Faculty of Economics, University of Cambridge.
    16. Fausto Cavalli & Mario Gilli & Ahmad Naimzada, 2025. "The role of polarization and hostility on equilibria in a simple class of symmetric conflict models," Theory and Decision, Springer, vol. 98(1), pages 61-83, February.
    17. de Roos, Nicolas & Matros, Alexander & Smirnov, Vladimir & Valencia, Zehra, 2022. "Choosing the Prize in Contests," Working Papers 2022-04, University of Sydney, School of Economics.

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    More about this item

    Keywords

    Contests; endogenous prize; existence and uniqueness; Subject Classification: D72; Subject Classification: C72; Subject Classification: L13;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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