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Modifying Variability and Correlations in Winner-Take-All Contests

Author

Listed:
  • Anil Gaba

    (INSEAD, 1 Ayer Rajah Avenue, Singapore 138676)

  • Ilia Tsetlin

    (INSEAD, 1 Ayer Rajah Avenue, Singapore 138676)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708-0120)

Abstract

We consider contests with a fixed proportion of winners based on relative performance. Special attention is paid to winner-take-all contests, which we define as contests with relatively few winners receiving relatively large awards, but we consider the full range of values of the proportion of winners. If a contestant has the opportunity to modify the distribution of her performance, what strategy is advantageous? When the proportion of winners is less than one-half, a riskier performance distribution is preferred; when this proportion is greater than one-half, it is better to choose a less risky distribution. Using a multinormal model, we consider modifications in the variability of the distribution and in correlations with the performance of other contestants. Increasing variability and decreasing correlations lead to improved chances of winning when the proportion of winners is less than one-half, and the opposite directions should be taken for proportions greater than one-half. Thus, it is better to take chances and to attempt to distance oneself from the other contestants (i.e., to break away from the herd) when there are few winners; a more conservative, herding strategy makes sense when there are many winners. Our analytical and numerical results indicate that the probability of winning can change substantially as variability and/or correlations are modified. Furthermore, in a game-theoretic setting in which all contestants can make modifications, choosing a riskier (less risky) performance distribution when the proportion of winners is low (high) is the dominant best-response strategy. We briefly consider some practical issues related to the recommended strategies and some possible extensions.

Suggested Citation

  • Anil Gaba & Ilia Tsetlin & Robert L. Winkler, 2004. "Modifying Variability and Correlations in Winner-Take-All Contests," Operations Research, INFORMS, vol. 52(3), pages 384-395, June.
  • Handle: RePEc:inm:oropre:v:52:y:2004:i:3:p:384-395
    DOI: 10.1287/opre.1030.0098
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    References listed on IDEAS

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    Cited by:

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    2. Kenneth C. Lichtendahl, Jr. & Robert L. Winkler, 2007. "Probability Elicitation, Scoring Rules, and Competition Among Forecasters," Management Science, INFORMS, vol. 53(11), pages 1745-1755, November.
    3. Debapriya Jojo Paul & Julia Henker & Sian Owen, 2019. "The aggregate impacts of tournament incentives in experimental asset markets," Experimental Economics, Springer;Economic Science Association, vol. 22(2), pages 441-476, June.
    4. Sajid Ullah & Farman Ullah Khan & Laura-Mariana Cismaș & Muhammad Usman & Andra Miculescu, 2022. "Do Tournament Incentives Matter for CEOs to Be Environmentally Responsible? Evidence from Chinese Listed Companies," IJERPH, MDPI, vol. 19(1), pages 1-20, January.
    5. Konrad, Kai A., 2014. "Search duplication in research and design spaces — Exploring the role of local competition," International Journal of Industrial Organization, Elsevier, vol. 37(C), pages 222-228.
    6. Natalia Karelaia & Robin Hogarth, 2010. "The attraction of uncertainty: Interactions between skill and levels of uncertainty in market-entry games," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 141-166, October.
    7. Ivo Schedlinsky & Friedrich Sommer & Arnt Wöhrmann, 2016. "Risk-taking in tournaments: an experimental analysis," Journal of Business Economics, Springer, vol. 86(8), pages 837-866, November.
    8. Ilia Tsetlin & Robert L. Winkler, 2007. "Decision Making with Multiattribute Performance Targets: The Impact of Changes in Performance and Target Distributions," Operations Research, INFORMS, vol. 55(2), pages 226-233, April.
    9. Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2017. "Between First- and Second-Order Stochastic Dominance," Management Science, INFORMS, vol. 63(9), pages 2933-2947, September.
    10. Ayc{s}e Kocab{i}y{i}kou{g}lu & Ioana Popescu, 2007. "Managerial Motivation Dynamics and Incentives," Management Science, INFORMS, vol. 53(5), pages 834-848, May.
    11. Brendan Daley & Ruoyu Wang, 2018. "When to Release Feedback in a Dynamic Tournament," Decision Analysis, INFORMS, vol. 15(1), pages 11-26, March.
    12. Zhang, Kun & Yang, Xiaolan & Gao, Mei, 2023. "When to use tournament incentives? Evidence from an investment experiment," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    13. Phillip E. Pfeifer, 2016. "The promise of pick-the-winners contests for producing crowd probability forecasts," Theory and Decision, Springer, vol. 81(2), pages 255-278, August.
    14. Philip Brookins & Jennifer Brown & Dmitry Ryvkin, 2016. "Peer Information and Risk-taking under Competitive and Non-competitive Pay Schemes," NBER Working Papers 22486, National Bureau of Economic Research, Inc.
    15. Cui, Xuegang & Feltovich, Nick & Zhang, Kun, 2022. "Incentive schemes, framing, and market behaviour: Evidence from an asset-market experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 301-324.
    16. Scott M Gilpatric, 2009. "Risk Taking In Contests And The Role Of Carrots And Sticks," Economic Inquiry, Western Economic Association International, vol. 47(2), pages 266-277, April.
    17. Enrico Lupi, 2024. "The impact of a winner takes all tournament on managers’ strategies and asset mispricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 121-136, June.
    18. Usvitskiy, Alexander, 2022. "Strategic risk-taking in dynamic contests," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 511-534.
    19. Fang, Dawei & Holmén, Martin & Kleinlercher, Daniel & Kirchler, Michael, 2017. "How tournament incentives affect asset markets: A comparison between winner-take-all tournaments and elimination contests," Journal of Economic Dynamics and Control, Elsevier, vol. 75(C), pages 1-27.

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