IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v213y2023ics0022053123000121.html
   My bibliography  Save this article

Optimal contest design: Tuning the heat

Author

Listed:
  • Letina, Igor
  • Liu, Shuo
  • Netzer, Nick

Abstract

We consider the design of contests when the principal can choose both the prize profile and how the prizes are allocated as a function of a possibly noisy signal about the agents' efforts. We provide sufficient conditions that guarantee optimality of a contest. Optimal contests have a minimally competitive prize profile and an intermediate degree of competitiveness in the contest success function. Whenever observation is not too noisy, the optimum can be achieved by an all-pay contest with a cap. When observation is perfect, the optimum can also be achieved by a nested Tullock contest. We relate our results to a recent literature which has asked similar questions but has typically focused on the design of either the prize profile or the contest success function.

Suggested Citation

  • Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
  • Handle: RePEc:eee:jetheo:v:213:y:2023:i:c:s0022053123000121
    DOI: 10.1016/j.jet.2023.105616
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053123000121
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jet.2023.105616?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    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. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    3. Letina, Igor & Liu, Shuo & Netzer, Nick, 2020. "Delegating performance evaluation," Theoretical Economics, Econometric Society, vol. 15(2), May.
    4. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, Decembrie.
    5. 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.
    6. Margaret A. Meyer, 1991. "Learning from Coarse Information: Biased Contests and Career Profiles," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 15-41.
    7. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    8. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    9. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    10. Jean-Michel Benkert & Igor Letina, 2020. "Designing Dynamic Research Contests," American Economic Journal: Microeconomics, American Economic Association, vol. 12(4), pages 270-289, November.
    11. Avinash Dixit, 2008. "Strategic Behavior in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 431-438, Springer.
    12. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    13. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    14. John Morgan & Henrik Orzen & Martin Sefton, 2012. "Endogenous entry in contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 435-463, October.
    15. Aner Sela, 2020. "Optimal allocations of prizes and punishments in Tullock contests," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 749-771, September.
    16. 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).
    17. 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.
    18. 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.
    19. Jun Xiao, 2012. "Asymmetric All-Pay Contests with Heterogeneous," Department of Economics - Working Papers Series 1151, The University of Melbourne.
    20. 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.
    21. Liu, Bin & Lu, Jingfeng, 2019. "The optimal allocation of prizes in contests with costly entry," International Journal of Industrial Organization, Elsevier, vol. 66(C), pages 137-161.
    22. Shi, Xianwen, 2012. "Optimal auctions with information acquisition," Games and Economic Behavior, Elsevier, vol. 74(2), pages 666-686.
    23. Aner Sela & Maya Amiad, 2016. "The Optimal Allocation Of Punishments In Tullock Contests," Working Papers 1613, Ben-Gurion University of the Negev, Department of Economics.
    24. Franke, Jörg & Leininger, Wolfgang & Wasser, Cédric, 2018. "Optimal favoritism in all-pay auctions and lottery contests," European Economic Review, Elsevier, vol. 104(C), pages 22-37.
    25. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    26. Lewis, Tracy R & Sappington, David E M, 1994. "Supplying Information to Facilitate Price Discrimination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 309-327, May.
    27. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    28. Sahm, Marco, 2022. "Optimal accuracy of unbiased Tullock contests with two heterogeneous players," BERG Working Paper Series 175, Bamberg University, Bamberg Economic Research Group.
    29. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    30. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    31. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    32. Jorge Lemus & Guillermo Marshall, 2021. "Dynamic Tournament Design: Evidence from Prediction Contests," Journal of Political Economy, University of Chicago Press, vol. 129(2), pages 383-420.
    33. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    34. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    35. 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.
    36. Justin P. Johnson & David P. Myatt, 2006. "On the Simple Economics of Advertising, Marketing, and Product Design," American Economic Review, American Economic Association, vol. 96(3), pages 756-784, June.
    37. Jack Hirshleifer, 1989. "Conflict and rent-seeking success functions: Ratio vs. difference models of relative success," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 251-262, Springer.
    38. Marco Sahm, 2022. "Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players," CESifo Working Paper Series 9601, CESifo.
    39. 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.
    40. Dawei Fang & Thomas Noe, 2022. "Less Competition, More Meritocracy?," Journal of Labor Economics, University of Chicago Press, vol. 40(3), pages 669-701.
    41. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    42. Clark, Derek J & Riis, Christian, 1996. "A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-184, April.
    43. Clark, Derek J. & Riis, Christian, 1998. "Influence and the discretionary allocation of several prizes," European Journal of Political Economy, Elsevier, vol. 14(4), pages 605-625, November.
    44. Feng, Xin & Lu, Jingfeng, 2018. "How to split the pie: Optimal rewards in dynamic multi-battle competitions," Journal of Public Economics, Elsevier, vol. 160(C), pages 82-95.
    45. Marco Sahm, 2022. "Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players," Games, MDPI, vol. 13(2), pages 1-6, March.
    46. Qiang Fu & Qian Jiao & Jingfeng Lu, 2015. "Contests with endogenous entry," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 387-424, May.
    47. Jorge Lemus & Emil Temnyalov, 2019. "Diversification and Information in Contests," Working Paper Series 2019/12, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    48. Dawei Fang & Thomas Noe & Philipp Strack, 2020. "Turning Up the Heat: The Discouraging Effect of Competition in Contests," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1940-1975.
    49. Wang Zhewei, 2010. "The Optimal Accuracy Level in Asymmetric Contests," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-18, April.
    50. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    51. Liu, Bin & Lu, Jingfeng & Wang, Ruqu & Zhang, Jun, 2018. "Optimal prize allocation in contests: The role of negative prizes," Journal of Economic Theory, Elsevier, vol. 175(C), pages 291-317.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Thomas Giebe & Oliver Gürtler, 2024. "Player Strength and Effort in Contests," ECONtribute Discussion Papers Series 285, University of Bonn and University of Cologne, Germany.
    3. Enzo Brox & Daniel Goller, 2024. "Tournaments, Contestant Heterogeneity and Performance," Papers 2401.05210, arXiv.org.
    4. Sumit Goel, 2022. "Optimal grading contests," Papers 2205.05207, arXiv.org, revised Sep 2023.
    5. 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.
    6. Huang, Ying & Jiao, Qian & Shen, Bo & Sun, Xiang, 2023. "Conflicts in regular networks," Journal of Mathematical Economics, Elsevier, vol. 106(C).

    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. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    2. 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.
    3. 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.
    4. Name Correa, Alvaro J. & Yildirim, Huseyin, 2024. "Multiple prizes in tournaments with career concerns," Journal of Economic Theory, Elsevier, vol. 215(C).
    5. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    6. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    7. 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.
    8. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    9. Sela, Aner, 2016. "The Optimal Allocation of Punishments in Tullock Contests," CEPR Discussion Papers 11592, C.E.P.R. Discussion Papers.
    10. 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.
    11. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    12. Aner Sela, 2020. "Optimal allocations of prizes and punishments in Tullock contests," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 749-771, September.
    13. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    14. Sakshi Gupta & Ram Singh, 2018. "On Existence and Properties of Pure-strategy Equilibria under Contests," Working Papers id:12840, eSocialSciences.
    15. Giebe, Thomas & Schweinzer, Paul, 2014. "Consuming your way to efficiency: Public goods provision through non-distortionary tax lotteries," European Journal of Political Economy, Elsevier, vol. 36(C), pages 1-12.
    16. 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).
    17. Yizhaq Minchuk & Aner Sela, 2021. "Subsidy and Taxation in All-Pay Auctions under Incomplete," Working Papers 2104, Ben-Gurion University of the Negev, Department of Economics.
    18. Shanglyu Deng & Hanming Fang & Qiang Fu & Zenan Wu, 2023. "Information Favoritism and Scoring Bias in Contests," PIER Working Paper Archive 23-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    19. 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.
    20. Letina, Igor & Liu, Shuo & Netzer, Nick, 2020. "Delegating performance evaluation," Theoretical Economics, Econometric Society, vol. 15(2), May.

    More about this item

    Keywords

    Contest design; Optimal contests; Tournaments;
    All these keywords.

    JEL classification:

    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

    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:eee:jetheo:v:213:y:2023:i:c:s0022053123000121. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.