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Optimality of winner-take-all contests: the role of attitudes toward risk

Author

Listed:
  • Liqun Liu

    (Texas A&M University [College Station])

  • Nicolas Treich

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper studies the role of risk attitudes in determining the optimality of winner-take-all contests. We compare the typical single-winner lottery contest with two alternatives, both spreading the rewards to more players: through holding multiple prize-giving lottery competitions or through guaranteeing a bottom prize for the losers. In the first comparison, we find that the multiple-competition contest is as effective as the winner-take-all contest when the contestants are risk neutral, but the former induces more effort than the latter when the contestants are both risk averse and prudent. In the second comparison, we find that the contest with a bottom prize is always dominated by the winner-take-all contest when the contestants are risk neutral, but the former could have an advantage over the latter when the contestants are both risk averse and prudent, and it is more likely so as the contestants become more prudent.

Suggested Citation

  • Liqun Liu & Nicolas Treich, 2021. "Optimality of winner-take-all contests: the role of attitudes toward risk," Post-Print hal-03722083, HAL.
  • Handle: RePEc:hal:journl:hal-03722083
    DOI: 10.1007/s11166-021-09355-8
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    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. Liqun Liu & Andrew Rettenmaier & Thomas Saving, 2009. "Conditional payments and self-protection," Journal of Risk and Uncertainty, Springer, vol. 38(2), pages 159-172, April.
    3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    4. Menegatti, Mario, 2009. "Optimal prevention and prudence in a two-period model," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 393-397, November.
    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. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    7. Richard Cornes & Roger Hartley, 2012. "Risk aversion in symmetric and asymmetric contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 247-275, October.
    8. Denuit, Michel & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," LIDAM Discussion Papers ISBA 2010010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Nicolas Treich, 2010. "Risk-aversion and prudence in rent-seeking games," Public Choice, Springer, vol. 145(3), pages 339-349, December.
    10. Denuit, Michel M. & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2027-2036, September.
    11. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    12. Dickson, Alex & MacKenzie, Ian A. & Sekeris, Petros G., 2018. "Rent-seeking incentives in share contests," Journal of Public Economics, Elsevier, vol. 166(C), pages 53-62.
    13. Liu, Liqun & Wong, Kit Pong, 2019. "Greater Arrow–Pratt (Absolute) risk aversion of higher orders," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 112-124.
    14. Liqun Liu & William S. Neilson, 2019. "Alternative Approaches to Comparative n th-Degree Risk Aversion," Management Science, INFORMS, vol. 65(8), pages 3824-3834, August.
    15. Paan Jindapon & Christopher Whaley, 2015. "Risk lovers and the rent over-investment puzzle," Public Choice, Springer, vol. 164(1), pages 87-101, July.
    16. Denuit, Michel & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes : an extension," LIDAM Discussion Papers ISBA 2010047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Neil Vousden & Ngo Van Long, 2008. "Risk-averse rent seeking with shared rents," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 293-307, Springer.
    18. Lee, Kangoh, 1998. "Risk Aversion and Self-Insurance-cum-Protection," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 139-150, November.
    19. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
    20. Qiang Fu & Jingfeng Lu & Yue Pan, 2015. "Team Contests with Multiple Pairwise Battles," American Economic Review, American Economic Association, vol. 105(7), pages 2120-2140, July.
    21. Cary Deck & Harris Schlesinger, 2010. "Exploring Higher Order Risk Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1403-1420.
    22. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    23. Michel M Denuit & Louis Eeckhoudt & Liqun Liu & Jack Meyer, 2016. "Tradeoffs for Downside Risk-Averse Decision-Makers and the Self-Protection Decision," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(1), pages 19-47, March.
    24. Charles N. Noussair & Stefan T. Trautmann & Gijs van de Kuilen, 2014. "Higher Order Risk Attitudes, Demographics, and Financial Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 325-355.
    25. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    26. Sebastian Ebert & Daniel Wiesen, 2011. "Testing for Prudence and Skewness Seeking," Management Science, INFORMS, vol. 57(7), pages 1334-1349, July.
    27. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    28. Dionne, Georges & Eeckhoudt, Louis, 1985. "Self-insurance, self-protection and increased risk aversion," Economics Letters, Elsevier, vol. 17(1-2), pages 39-42.
    29. Chowdhury, Subhasish M. & Kim, Sang-Hyun, 2014. "A note on multi-winner contest mechanisms," Economics Letters, Elsevier, vol. 125(3), pages 357-359.
    30. Schroyen, Fred & Treich, Nicolas, 2016. "The power of money: Wealth effects in contests," Games and Economic Behavior, Elsevier, vol. 100(C), pages 46-68.
    31. Peter, Richard, 2017. "Optimal self-protection in two periods: On the role of endogenous saving," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 19-36.
    32. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    33. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    34. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    35. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    36. Jindapon, Paan & Yang, Zhe, 2017. "Risk attitudes and heterogeneity in simultaneous and sequential contests," Journal of Economic Behavior & Organization, Elsevier, vol. 138(C), pages 69-84.
    37. Skaperdas, Stergios & Gan, Li, 1995. "Risk Aversion in Contests," Economic Journal, Royal Economic Society, vol. 105(431), pages 951-962, July.
    38. Jindapon, Paan & Neilson, William S., 2007. "Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 719-728, September.
    39. Cason, Timothy N. & Masters, William A. & Sheremeta, Roman M., 2020. "Winner-take-all and proportional-prize contests: Theory and experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 175(C), pages 314-327.
    40. Sahm, Marco, 2017. "Risk aversion and prudence in contests," BERG Working Paper Series 120, Bamberg University, Bamberg Economic Research Group.
    41. O'Keeffe, Mary & Viscusi, W Kip & Zeckhauser, Richard J, 1984. "Economic Contests: Comparative Reward Schemes," Journal of Labor Economics, University of Chicago Press, vol. 2(1), pages 27-56, January.
    42. Crainich, David & Eeckhoudt, Louis & Menegatti, Mario, 2016. "Changing risks and optimal effort," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 97-106.
    43. David Crainich & Louis Eeckhoudt, 2008. "On the intensity of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 267-276, June.
    44. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    45. Dionne, Georges & Li, Jingyuan, 2011. "The impact of prudence on optimal prevention revisited," Economics Letters, Elsevier, vol. 113(2), pages 147-149.
    46. Chiu, W.Henry, 2005. "Degree of downside risk aversion and self-protection," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 93-101, February.
    47. Marco Sahm, 2017. "Risk aversion and prudence in contests," Economics Bulletin, AccessEcon, vol. 37(2), pages 1122-1132.
    48. Ilia Tsetlin & Anil Gaba & Robert L. Winkler, 2004. "Strategic Choice of Variability in Multiround Contests and Contests with Handicaps," Journal of Risk and Uncertainty, Springer, vol. 29(2), pages 143-158, September.
    49. 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.
    50. Clark, Derek J & Riis, Christian, 1996. "A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-184, April.
    51. 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.
    52. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    53. Louis Eeckhoudt & Christian Gollier, 2005. "The impact of prudence on optimal prevention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 989-994, November.
    54. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    55. Donald C. Keenan & Arthur Snow, 2016. "Strong Increases in Downside Risk Aversion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(2), pages 149-161, September.
    56. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    57. Marco Sahm, 2017. "Risk Aversion and Prudence in Contests," CESifo Working Paper Series 6417, CESifo.
    58. Ebert, Sebastian, 2015. "On skewed risks in economic models and experiments," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 85-97.
    59. Qiang Fu & Jingfeng Lu, 2012. "The optimal multi-stage contest," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 351-382, October.
    60. Liqun Liu & Jack Meyer & Andrew J. Rettenmaier & Thomas R. Saving, 2018. "Risk and risk aversion effects in contests with contingent payments," Journal of Risk and Uncertainty, Springer, vol. 56(3), pages 289-305, June.
    61. 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.
    62. Li, Jingyuan, 2009. "Comparative higher-degree Ross risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 333-336, December.
    63. Pavlo Blavatskyy, "undated". "Why the Olympics have three prizes and not just one," IEW - Working Papers 200, Institute for Empirical Research in Economics - University of Zurich.
    64. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    65. Konrad, Kai A & Schlesinger, Harris, 1997. "Risk Aversion in Rent-Seeking and Rent-Augmenting Games," Economic Journal, Royal Economic Society, vol. 107(445), pages 1671-1683, November.
    66. Berry, S Keith, 1993. "Rent-Seeking with Multiple Winners," Public Choice, Springer, vol. 77(2), pages 437-443, October.
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    More about this item

    Keywords

    Contests; Winner-take-all; Multiple prizes; Risk aversion; Prudence;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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