IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v175y2018icp291-317.html
   My bibliography  Save this article

Optimal prize allocation in contests: The role of negative prizes

Author

Listed:
  • Liu, Bin
  • Lu, Jingfeng
  • Wang, Ruqu
  • Zhang, Jun

Abstract

In this paper, we analyze the role of negative prizes in contest design with a fixed budget, risk-neutral contestants, and independent private abilities. The effort-maximizing prize allocation rule features a threshold. When the highest effort is above the threshold, all contestants with lower efforts receive negative prizes. These negative prizes are used to augment the prize to the contestant with the highest effort, which better incentivizes contestants with higher abilities. When no contestant's effort exceeds the threshold, all contestants equally split the initial budget (or a portion of it) to ensure their participation. We find that allowing negative prizes can increase the expected total effort dramatically. In particular, if no bound is imposed on negative prizes, the expected total effort can be arbitrarily close to the highest possible effort inducible when all contestants have the maximum ability with certainty. The above contest is shown to be the optimal mechanism for a more general class of mechanisms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:175:y:2018:i:c:p:291-317
    DOI: 10.1016/j.jet.2018.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053118300243
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2018.01.016?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 search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Yi‐Chun Chen & Siyang Xiong, 2013. "Genericity and Robustness of Full Surplus Extraction," Econometrica, Econometric Society, vol. 81(2), pages 825-847, March.
    4. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, January.
    5. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    6. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 338-363.
    7. Michael Peters, 2001. "Surplus Extraction and Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 613-631.
    8. Leonid Polishchuk & Alexander Tonis, 2013. "Endogenous contest success functions: a mechanism design approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 271-297, January.
    9. Robert, Jacques, 1991. "Continuity in auction design," Journal of Economic Theory, Elsevier, vol. 55(1), pages 169-179, October.
    10. Kirkegaard, René, 2012. "Favoritism in asymmetric contests: Head starts and handicaps," Games and Economic Behavior, Elsevier, vol. 76(1), pages 226-248.
    11. Jean-Jacques Laffont & David Martimort, 2000. "Mechanism Design with Collusion and Correlation," Econometrica, Econometric Society, vol. 68(2), pages 309-342, March.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    13. 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.
    14. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    15. 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.
    16. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
    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. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    2. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    3. Paul Pecorino, 2020. "Bridge burning and escape routes," Public Choice, Springer, vol. 184(3), pages 399-414, September.
    4. Name Correa, Alvaro J. & Yildirim, Huseyin, 2024. "Multiple prizes in tournaments with career concerns," Journal of Economic Theory, Elsevier, vol. 215(C).
    5. 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.
    6. Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).
    7. Boyarchenko, Svetlana, 2021. "Inefficiency of sponsored research," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    8. Mengxi Zhang, 2023. "Optimal Contests with Incomplete Information and Convex Effort Costs," CRC TR 224 Discussion Paper Series crctr224_2023_156v2, University of Bonn and University of Mannheim, Germany.
    9. Feng, Xin & Jiao, Qian & Kuang, Zhonghong & Lu, Jingfeng, 2024. "Optimal prize design in team contests with pairwise battles," Journal of Economic Theory, Elsevier, vol. 215(C).
    10. Xiao, Jun, 2023. "Ability grouping in contests," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    11. Andrzej Baranski & Sumit Goel, 2024. "Contest design with a finite type-space: A unifying approach," Papers 2410.04970, arXiv.org, revised Oct 2024.
    12. 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.
    13. Aner Sela & Yizhaq Minchuk, 2024. "Carrots and sticks: collaboration of taxation and subsidies in contests," Working Papers 2407, Ben-Gurion University of the Negev, Department of Economics.
    14. Ginzburg, Boris, 2019. "A Simple Model of Competitive Testing," MPRA Paper 99463, University Library of Munich, Germany.

    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, Hu & Haghpanah, Nima & Hartline, Jason & Kleinberg, Robert, 2021. "Full surplus extraction from samples," Journal of Economic Theory, Elsevier, vol. 193(C).
    2. Aner Sela & Yizhaq Minchuk, 2024. "Carrots and sticks: collaboration of taxation and subsidies in contests," Working Papers 2407, Ben-Gurion University of the Negev, Department of Economics.
    3. Minchuk, Yizhaq & Sela, Aner, 2023. "Subsidy and taxation in all-pay auctions under incomplete information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 99-114.
    4. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    5. Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).
    6. Lopomo, Giuseppe & Rigotti, Luca & Shannon, Chris, 2022. "Uncertainty and robustness of surplus extraction," Journal of Economic Theory, Elsevier, vol. 199(C).
    7. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. 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.
    9. Krajbich, Ian & Camerer, Colin & Rangel, Antonio, 2017. "Exploring the scope of neurometrically informed mechanism design," Games and Economic Behavior, Elsevier, vol. 101(C), pages 49-62.
    10. 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.
    11. Yamashita, Takuro, 2018. "Revenue guarantees in auctions with a (correlated) common prior and additional information," TSE Working Papers 18-937, Toulouse School of Economics (TSE).
    12. Obara Ichiro, 2008. "The Full Surplus Extraction Theorem with Hidden Actions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-28, March.
    13. Chawla, Shuchi & Hartline, Jason D. & Sivan, Balasubramanian, 2019. "Optimal crowdsourcing contests," Games and Economic Behavior, Elsevier, vol. 113(C), pages 80-96.
    14. Olivier Compte & Philippe Jehiel, 2009. "Veto Constraint in Mechanism Design: Inefficiency with Correlated Types," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 182-206, February.
    15. Gizatulina, Alia & Hellwig, Martin, 2010. "Informational smallness and the scope for limiting information rents," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2260-2281, November.
    16. Menicucci, Domenico, 2006. "Full surplus extraction by a risk averse seller in correlated environments," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 280-300, May.
    17. Krähmer, Daniel, 2012. "Auction design with endogenously correlated buyer types," Journal of Economic Theory, Elsevier, vol. 147(1), pages 118-141.
    18. Guo, Huiyi, 2024. "Collusion-proof mechanisms for full surplus extraction," Games and Economic Behavior, Elsevier, vol. 145(C), pages 263-284.
    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. Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July.

    More about this item

    Keywords

    Optimal contest; Mechanism design; Negative prize; Incomplete information; Cross transfer; Leverage;
    All these keywords.

    JEL classification:

    • 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
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:175:y:2018:i:c:p:291-317. 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.