[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/abo/neswpt/w0250.html
   My bibliography  Save this paper

Tournament Rewards and Heavy Tails

Author

Listed:
  • Mikhail Drugov

    (New Economic School and CEPR)

  • Dmitry Ryvkin

    (Department of Economics, Florida State University)

Abstract
Heavy-tailed fluctuations are common in many environments, such as sales of creative and innovative products or the financial sector. We study how the presence of heavy tails in the distribution of shocks affects the optimal allocation of prizes in rank-order tournaments. While a winner-take-all prize schedule maximizes aggregate effort for light-tailed shocks, prize sharing becomes optimal when shocks acquire heavy tails, increasingly so following a skewness order. Extreme prize sharing { rewarding all ranks but the very last { is optimal when shocks have a decreasing failure rate, such as power laws. Hence, under heavy-tailed uncertainty, typically associated with strong inequality in the distribution of gains, providing incentives and reducing inequality go hand in hand.

Suggested Citation

  • Mikhail Drugov & Dmitry Ryvkin, 2018. "Tournament Rewards and Heavy Tails," Working Papers w0250, New Economic School (NES).
    • Handle: RePEc:abo:neswpt:w0250
    as

    Download full text from publisher

    File URL: https://www.nes.ru/files/Preprints-resh/WP250.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Alberto Alesina & Dani Rodrik, 1994. "Distributive Politics and Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 465-490.
    2. 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.
    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. 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.
    5. Letina, Igor & Liu, Shuo & Netzer, Nick, 2020. "Delegating performance evaluation," Theoretical Economics, Econometric Society, vol. 15(2), May.
    6. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    7. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    8. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    9. 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.
    10. Judith Chevalier & Austan Goolsbee, 2003. "Measuring Prices and Price Competition Online: Amazon.com and BarnesandNoble.com," Quantitative Marketing and Economics (QME), Springer, vol. 1(2), pages 203-222, June.
    11. 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.
    12. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    13. 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.
    14. David Gill & Zdenka Kissová & Jaesun Lee & Victoria Prowse, 2019. "First-Place Loving and Last-Place Loathing: How Rank in the Distribution of Performance Affects Effort Provision," Management Science, INFORMS, vol. 65(2), pages 494-507, February.
    15. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    16. John D. Huber & Laura Mayoral, 2019. "Group inequality and the severity of civil conflict," Journal of Economic Growth, Springer, vol. 24(1), pages 1-41, March.
    17. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    18. Dutcher, E. Glenn & Balafoutas, Loukas & Lindner, Florian & Ryvkin, Dmitry & Sutter, Matthias, 2015. "Strive to be first or avoid being last: An experiment on relative performance incentives," Games and Economic Behavior, Elsevier, vol. 94(C), pages 39-56.
    19. 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.
    20. Christian Terwiesch & Yi Xu, 2008. "Innovation Contests, Open Innovation, and Multiagent Problem Solving," Management Science, INFORMS, vol. 54(9), pages 1529-1543, September.
    21. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    22. Dubey, Pradeep & Geanakoplos, John, 2010. "Grading exams: 100,99,98,... or A,B,C?," Games and Economic Behavior, Elsevier, vol. 69(1), pages 72-94, May.
    23. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    24. Canice Prendergast, 1999. "The Provision of Incentives in Firms," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 7-63, March.
    25. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    26. Hefti, Andreas, 2017. "Equilibria in symmetric games: theory and applications," Theoretical Economics, Econometric Society, vol. 12(3), September.
    27. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    28. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 338-363.
    29. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    30. Clark, Derek J & Riis, Christian, 1996. "A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-184, April.
    31. 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.
    32. Lee, Sam-Ho, 2014. "The incentive effect of coarsening the competition structure in a tournament," Economics Letters, Elsevier, vol. 125(3), pages 411-414.
    33. 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.
    34. 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.
    35. Eduardo M. Azevedo & Alex Deng & José Luis Montiel Olea & Justin Rao & E. Glen Weyl, 2020. "A/B Testing with Fat Tails," Journal of Political Economy, University of Chicago Press, vol. 128(12), pages 4614-4000.
    36. Rosen, Sherwin, 1981. "The Economics of Superstars," American Economic Review, American Economic Association, vol. 71(5), pages 845-858, December.
    37. 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.
    38. David R. Roberts, 1956. "A General Theory of Executive Compensation Based on Statistically Tested Propositions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(2), pages 270-294.
    39. Kostas Bimpikis & Mihalis G. Markakis, 2016. "Inventory Pooling Under Heavy-Tailed Demand," Management Science, INFORMS, vol. 62(6), pages 1800-1813, June.
    40. Robert H. Frank, 2016. "Success and Luck: Good Fortune and the Myth of Meritocracy," Economics Books, Princeton University Press, edition 1, number 10663.
    41. Laurence Ales & Soo-Haeng Cho & Ersin Körpeoğlu, 2017. "Optimal Award Scheme in Innovation Tournaments," Operations Research, INFORMS, vol. 65(3), pages 693-702, June.
    42. Lazear, Edward P, 1999. "Personnel Economics: Past Lessons and Future Directions: Presidential Address to the Society of Labor Economists, San Francisco, May 1, 1998," Journal of Labor Economics, University of Chicago Press, vol. 17(2), pages 199-236, April.
    43. Edward P. Lazear, 1999. "Personnel Economics: Past Lessons and Future Directions," NBER Working Papers 6957, National Bureau of Economic Research, Inc.
    44. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
    45. Yigal Gerchak & Qi-Ming He, 2003. "When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 151-165.
    46. Ajay Kalra & Mengze Shi, 2001. "Designing Optimal Sales Contests: A Theoretical Perspective," Marketing Science, INFORMS, vol. 20(2), pages 170-193, December.
    47. Marina Halac & Navin Kartik & Qingmin Liu, 2017. "Contests for Experimentation," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1523-1569.
    48. Kirkegaard, René, 2017. "A unifying approach to incentive compatibility in moral hazard problems," Theoretical Economics, Econometric Society, vol. 12(1), January.
    49. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    50. Kadan, Ohad & Swinkels, Jeroen M., 2013. "On the moral hazard problem without the first-order approach," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2313-2343.
    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. Mert Kimya, 2024. "Power, Status and the Stability of Hierarchies," Working Papers 2024-04, University of Sydney, School of Economics.
    2. Lu, Jingfeng & Wang, Zhewei & Zhou, Lixue, 2022. "Optimal favoritism in contests with identity-contingent prizes," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 40-50.
    3. Name Correa, Alvaro J. & Yildirim, Huseyin, 2024. "Multiple prizes in tournaments with career concerns," Journal of Economic Theory, Elsevier, vol. 215(C).
    4. Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).
    5. Doron Klunover, 2020. "Nice guys don't always finish last: succeeding in hierarchical organizations," Papers 2007.04435, arXiv.org, revised Sep 2020.
    6. 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.
    7. Song, Jian & Houser, Daniel, 2023. "Asymmetric shocks in contests: Theory and experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 243-267.
    8. Mikhail Drugov & Dmitry Ryvkin, 2019. "The shape of luck and competition in tournaments," Working Papers w0251, Center for Economic and Financial Research (CEFIR).
    9. Aner Sela & Ishay Rabi & Chen Cohen, 2024. "Reputation in Contests," Working Papers 2409, Ben-Gurion University of the Negev, Department of Economics.
    10. 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.
    11. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    12. Zhu, Weichao & Wang, Lu & Lang, Youze, 2022. "The costs and benefits of tournament in a frictional labor market," Economic Modelling, Elsevier, vol. 113(C).
    13. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    14. 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.
    15. Andrzej Baranski & Sumit Goel, 2024. "Contest design with a finite type-space: A unifying approach," Papers 2410.04970, arXiv.org, revised Oct 2024.
    16. Nicolas de Roos & Alexander Matros & Vladimir Smirnov, 2024. "Elimination tournaments with resource constraints," Working Papers 2024-06, University of Sydney, School of Economics.
    17. Yildirim, Mustafa, 2023. "When does division matter? Revisiting the optimal contest architecture," Economics Letters, Elsevier, vol. 230(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. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    2. 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.
    3. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    4. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Optimal Tournaments," CEPR Discussion Papers 12368, C.E.P.R. Discussion Papers.
    5. Mikhail Drugov & Dmitry Ryvkin, 2019. "The shape of luck and competition in tournaments," Working Papers w0251, Center for Economic and Financial Research (CEFIR).
    6. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    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. 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.
    9. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Winner-Take-All Tournaments," CEPR Discussion Papers 12067, C.E.P.R. Discussion Papers.
    10. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    11. Name Correa, Alvaro J. & Yildirim, Huseyin, 2024. "Multiple prizes in tournaments with career concerns," Journal of Economic Theory, Elsevier, vol. 215(C).
    12. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    13. 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.
    14. Minchuk, Yizhaq & Sela, Aner, 2014. "All-pay auctions with certain and uncertain prizes," Games and Economic Behavior, Elsevier, vol. 88(C), pages 130-134.
    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. Xiaotie Deng & Yotam Gafni & Ron Lavi & Tao Lin & Hongyi Ling, 2021. "From Monopoly to Competition: Optimal Contests Prevail," Papers 2107.13363, arXiv.org.
    18. Liqun Liu & Nicolas Treich, 2021. "Optimality of winner-take-all contests: the role of attitudes toward risk," Journal of Risk and Uncertainty, Springer, vol. 63(1), pages 1-25, August.
    19. Sela, Aner, 2016. "The Optimal Allocation of Punishments in Tullock Contests," CEPR Discussion Papers 11592, C.E.P.R. Discussion Papers.
    20. 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.

    More about this item

    Keywords

    heavy tails; power law; tournament; optimal allocation of prizes; failure rate;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

    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:abo:neswpt:w0250. 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: Vladimir Ivanyukhin (email available below). General contact details of provider: https://edirc.repec.org/data/nerasru.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.