IDEAS home Printed from https://ideas.repec.org/p/hhs/vxesta/2024_004.html

Player strength and effort in contests

Author

Listed:

Abstract

In competitive settings, disparities in player strength are common. It is intuitively unclear whether a stronger player would opt for larger or smaller effort compared to weaker players. Larger effort could leverage their strength, while lower effort might be justified by their higher probability of winning regardless of effort. We analyze contests with three or more players, exploring when stronger players exert larger or lower effort. To rank efforts, it suffices to compare marginal utilities in situations where efforts are equal. Effort ranking depends on differences in hazard rates (which are smaller for stronger players) and reversed hazard rates (which are larger for stronger players). Compared to weaker players, stronger players choose larger effort in winner-takes-all contests and lower effort in loser-gets-nothing contests. Effort rankings can be non-monotonic in contests with several identical prizes, and they depend on the slopes of players’ pdfs in contests with linear prize structure.

Suggested Citation

  • Giebe, Thomas & Gürtler, Oliver, 2024. "Player strength and effort in contests," Working Papers in Economics and Statistics 4/2024, Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
    • Handle: RePEc:hhs:vxesta:2024_004
    as

    Download full text from publisher

    File URL: https://ekonomihogskolan.lnu.se/vxesta/24-04_Player-strength-and-effort-in-contests.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    2. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    3. 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.
    4. Qiang Fu & Jingfeng Lu, 2012. "Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 497-517, March.
    5. Giebe, Thomas, 2014. "Innovation contests with entry auction," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 165-176.
    6. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    7. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    8. Seel, Christian, 2014. "The value of information in asymmetric all-pay auctions," Games and Economic Behavior, Elsevier, vol. 86(C), pages 330-338.
    9. René Kirkegaard, 2023. "Contest Design with Stochastic Performance," American Economic Journal: Microeconomics, American Economic Association, vol. 15(1), pages 201-238, February.
    10. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    11. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    12. 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).
    13. Robert Akerlof & Richard Holden, 2012. "The nature of tournaments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 289-313, October.
    14. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    15. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-289, March.
    16. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    17. Julio González-Díaz & Ron Siegel, 2013. "Matching and price competition: beyond symmetric linear costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 835-844, November.
    18. Zhang, Mengxi, 2024. "Optimal contests with incomplete information and convex effort costs," Theoretical Economics, Econometric Society, vol. 19(1), January.
    19. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    20. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    21. Fu, Qiang & Wu, Zenan, 2020. "On the optimal design of biased contests," Theoretical Economics, Econometric Society, vol. 15(4), November.
    22. Budde, Jörg, 2009. "Information in tournaments under limited liability," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 59-72, January.
    23. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
    24. Loukas Balafoutas & E. Glenn Dutcher & Florian Lindner & Dmitry Ryvkin, 2017. "The Optimal Allocation Of Prizes In Tournaments Of Heterogeneous Agents," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 461-478, January.
    25. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    26. Konrad, Kai A., 2002. "Investment in the absence of property rights; the role of incumbency advantages," European Economic Review, Elsevier, vol. 46(8), pages 1521-1537, September.
    27. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-890, September.
    28. Ramesh Gupta & N. Balakrishnan, 2012. "Log-concavity and monotonicity of hazard and reversed hazard functions of univariate and multivariate skew-normal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 181-191, February.
    29. Jeremy Bulow & Jonathan Levin, 2006. "Matching and Price Competition," American Economic Review, American Economic Association, vol. 96(3), pages 652-668, June.
    30. Qiang Fu & Zenan Wu & Yuxuan Zhu, 2023. "Bid Caps in Noisy Contests," American Economic Journal: Microeconomics, American Economic Association, vol. 15(3), pages 426-473, August.
    31. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, 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. 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.
    2. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    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. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    5. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    6. Giebe, Thomas & Gürtler, Oliver, 2026. "When is a contest "additive"? A characterization of strategic equivalence," Working Papers in Economics and Statistics 3/2026, Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
    7. Fu, Qiang & Wang, Xiruo & Wu, Zenan, 2021. "Multi-prize contests with risk-averse players," Games and Economic Behavior, Elsevier, vol. 129(C), pages 513-535.
    8. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    9. Cohen, Chen & Lagziel, David & Levi, Ofer & Sela, Aner, 2023. "The role of the second prize in all-pay auctions with two heterogeneous prizes," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    10. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    11. Stefano Barbieri & Marco Serena, 2024. "Centralized assignment of prizes and contestants," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 117-152, February.
    12. Chen Cohen & David Lagziel & Ofer Levi & Aner Sela, 2020. "All-Pay Auctions With Heterogeneous Prizes And Partially Asymmetric Players," Working Papers 2010, Ben-Gurion University of the Negev, Department of Economics.
    13. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    14. Loukas Balafoutas & E. Glenn Dutcher & Florian Lindner & Dmitry Ryvkin, 2017. "The Optimal Allocation Of Prizes In Tournaments Of Heterogeneous Agents," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 461-478, January.
    15. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2019. "A general framework for studying contests," MPRA Paper 97363, University Library of Munich, Germany.
    16. Aner Sela, 2002. "Contest Architecture (jointly with Benny Moldovanu)," Theory workshop papers 357966000000000088, UCLA Department of Economics.
    17. 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.
    18. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    19. Benny Moldovanu & Aner Sela & Xianwen Shi, 2012. "Carrots And Sticks: Prizes And Punishments In Contests," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 453-462, April.
    20. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:vxesta:2024_004. 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: Thomas Giebe (email available below). General contact details of provider: https://edirc.repec.org/data/inlnuse.html .

    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.