Journal of Risk and Uncertainty

, Volume 56, Issue 3, pp 289–305 | Cite as

Risk and risk aversion effects in contests with contingent payments

  • Liqun LiuEmail author
  • Jack Meyer
  • Andrew J. Rettenmaier
  • Thomas R. Saving


Contests by their very nature involve risk, winning and losing are both possible, and the gain from winning can itself be uncertain. The participants in a contest use resources to increase their chance of winning. The main focus of this analysis is on the effects of risk aversion and risk in contests where only winners pay for resources used to compete. When payment is contingent on winning, the effect of risk aversion is in the opposite direction of what occurs when costs are paid by both winners and losers. A number of contests observed in the marketplace that exhibit this contingent payment property are discussed.


Risk aversion Contests Contingent payments Self-protection Ross risk aversion Downside risk aversion 

JEL Classifications

C72 D72 D81 



We want to thank Adam Narkiewicz, Nicolas Treich, an anonymous reviewer, and the session participants at the 2017 EGRIE seminar in London, for very helpful comments and suggestions. All remaining errors are our own.


  1. Baye, M. R., Kovenock, D., & de Vries, C. G. (1996). The all-pay auction with complete information. Economic Theory, 8, 291–305.CrossRefGoogle Scholar
  2. Briys, E., & Schlesinger, H. (1990). Risk aversion and the propensities for self-insurance and self-protection. Southern Economic Journal, 57, 458–467.CrossRefGoogle Scholar
  3. Chiu, W. H. (2005). Degree of downside risk aversion and self-protection. Insurance: Mathematics and Economics, 36, 93–101.Google Scholar
  4. Cornes, R., & Hartley, R. (2012). Risk aversion in symmetric and asymmetric contests. Economic Theory, 51, 247–275.CrossRefGoogle Scholar
  5. Denuit, M., & Eeckhoudt, L. (2010). Stronger measures of higher-order risk attitudes. Journal of Economic Theory, 145, 2027–2036.CrossRefGoogle Scholar
  6. Denuit, M., Eeckhoudt, L., Liu, L., & Meyer, J. (2016). Tradeoffs for downside risk averse decision makers and the self-protection decision. Geneva Risk and Insurance Review, 41, 19–47.CrossRefGoogle Scholar
  7. Dionne, G., & Eeckhoudt, L. (1985). Self-insurance, self-protection, and increased risk aversion. Economics Letters, 17, 39–42.CrossRefGoogle Scholar
  8. Dionne, G., & Li, J. (2011). The impact of prudence on optimal prevention revisited. Economics Letters, 113, 147–149.CrossRefGoogle Scholar
  9. Ebert, S. (2015). On skewed risks in economic models and experiments. Journal of Economic Behavior and Organization, 112, 85–97.CrossRefGoogle Scholar
  10. Eeckhoudt, L., & Gollier, C. (2005). The impact of prudence on optimal prevention. Economic Theory, 26, 989–994.CrossRefGoogle Scholar
  11. Eeckhoudt, L., Liu, L., & Meyer, J. (2017). Restricted increases in risk aversion and their application. Economic Theory, 64, 161–181.CrossRefGoogle Scholar
  12. Ehrlich, I., & Becker, G. (1972). Market insurance and self-insurance. Journal of Political Economy, 80, 623–648.CrossRefGoogle Scholar
  13. Fu, Q., & Lu, J. (2010). Contest design and optimal endogenous entry. Economic Inquiry, 48, 80–88.CrossRefGoogle Scholar
  14. Gradstein, M., & Konrad, K. A. (1999). Orchestrating rent seeking contests. The Economic Journal, 109, 536–545.CrossRefGoogle Scholar
  15. Jindapon, P., & Neilson, W. S. (2007). Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach. Journal of Economic Theory, 136, 719–728.CrossRefGoogle Scholar
  16. Jindapon, P., & Whaley, C. A. (2015). Risk lovers and the rent over-investment puzzle. Public Choice, 164, 87–101.CrossRefGoogle Scholar
  17. Keenan, D. C., & Snow, A. (2016). Strong increases in downside risk aversion. Geneva Risk and Insurance Review, 41, 149–161.CrossRefGoogle Scholar
  18. Konrad, K., & Schlesinger, H. (1997). Risk aversion in rent-seeking and rent-augmenting games. The Economic Journal, 107, 1671–1683.CrossRefGoogle Scholar
  19. Li, J. (2009). Comparative higher-degree Ross risk aversion. Insurance: Mathematics and Economics, 45, 333–336.Google Scholar
  20. Liu, L., & Meyer, J. (2013). Substituting one risk increase for another: A method for measuring risk aversion. Journal of Economic Theory, 148, 2706–2718.CrossRefGoogle Scholar
  21. Liu, L., & Meyer, J. (2017). The increasing convex order and the tradeoff of size for risk. Journal of Risk and Insurance, 84, 881–897.CrossRefGoogle Scholar
  22. Liu, L., Rettenmaier, A. J., & Saving, T. R. (2009). Conditional payments and self-protection. Journal of Risk and Uncertainty, 38, 159–172.CrossRefGoogle Scholar
  23. Menegatti, M. (2009). Optimal prevention and prudence in a two-period model. Mathematical Social Science, 58, 393–397.CrossRefGoogle Scholar
  24. Menezes, C. F., Geiss, C., & Tressler, J. (1980). Increasing downside risk. American Economic Review, 70, 921–932.Google Scholar
  25. Modica, S., & Scarsini, M. (2005). A note on comparative downside risk aversion. Journal of Economic Theory, 122, 267–271.CrossRefGoogle Scholar
  26. Moldovanu, B., & Sela, A. (2001). The optimal allocation of prizes in contests. American Economic Review, 91, 542–558.CrossRefGoogle Scholar
  27. Nitzan, S. (1994). Modelling rent-seeking contests. European Journal of Political Economy, 10, 41–60.CrossRefGoogle Scholar
  28. Peter, R. (2017). Optimal self-protection in two periods: On the role of endogenous saving. Journal of Economic Behavior and Organization, 137, 19–36.CrossRefGoogle Scholar
  29. Pratt, J. (1964). Risk aversion in the small and in the large. Econometrica, 32, 122–136.CrossRefGoogle Scholar
  30. Ross, S. A. (1981). Some stronger measures of risk aversion in the small and in the large with applications. Econometrica, 49, 621–638.CrossRefGoogle Scholar
  31. Rothschild, M., & Stiglitz, J. E. (1970). Increasing risk: I. A definition. Journal of Economic Theory, 2(3), 225–243.CrossRefGoogle Scholar
  32. Sahm, M. (2017). Risk aversion and prudence in contests. Economics Bulletin, 37. Issue, 2, 1122–1132.Google Scholar
  33. Schroyen, F., & Treich, N. (2016). The power of money: Wealth effects in contests. Games and Economic Behavior, 100, 46–68.CrossRefGoogle Scholar
  34. Skaperdas, S. (1996). Contest success functions. Economic Theory, 7, 283–290.CrossRefGoogle Scholar
  35. Skaperdas, S., & Gan, L. (1995). Risk aversion in contests. The Economic Journal, 105, 951–962.CrossRefGoogle Scholar
  36. Treich, N. (2010). Risk-aversion and prudence in rent-seeking games. Public Choice, 145, 339–349.CrossRefGoogle Scholar
  37. Tullock, G. (1980). Efficient rent seeking. In J. M. Buchanan, R. D. Tollison, & G. Tullock (Eds.), Toward a theory of rent-seeking society. College Station: Texas A&M University Press.Google Scholar
  38. Yates, A. J. (2011). Winner-pay contests. Public Choice, 147, 93–106.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Liqun Liu
    • 1
    Email author
  • Jack Meyer
    • 2
  • Andrew J. Rettenmaier
    • 1
  • Thomas R. Saving
    • 1
  1. 1.Private Enterprise Research CenterTexas A&M UniversityCollege StationUSA
  2. 2.Department of EconomicsMichigan State UniversityEast LansingUSA

Personalised recommendations