# Risk and risk aversion effects in contests with contingent payments

- 148 Downloads

## Abstract

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.

## Keywords

Risk aversion Contests Contingent payments Self-protection Ross risk aversion Downside risk aversion## JEL Classifications

C72 D72 D81## Notes

### Acknowledgements

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.

## References

- Baye, M. R., Kovenock, D., & de Vries, C. G. (1996). The all-pay auction with complete information.
*Economic Theory, 8*, 291–305.CrossRefGoogle Scholar - Briys, E., & Schlesinger, H. (1990). Risk aversion and the propensities for self-insurance and self-protection.
*Southern Economic Journal, 57*, 458–467.CrossRefGoogle Scholar - Chiu, W. H. (2005). Degree of downside risk aversion and self-protection.
*Insurance: Mathematics and Economics, 36*, 93–101.Google Scholar - Cornes, R., & Hartley, R. (2012). Risk aversion in symmetric and asymmetric contests.
*Economic Theory, 51*, 247–275.CrossRefGoogle Scholar - Denuit, M., & Eeckhoudt, L. (2010). Stronger measures of higher-order risk attitudes.
*Journal of Economic Theory, 145*, 2027–2036.CrossRefGoogle Scholar - 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 - Dionne, G., & Eeckhoudt, L. (1985). Self-insurance, self-protection, and increased risk aversion.
*Economics Letters, 17*, 39–42.CrossRefGoogle Scholar - Dionne, G., & Li, J. (2011). The impact of prudence on optimal prevention revisited.
*Economics Letters, 113*, 147–149.CrossRefGoogle Scholar - Ebert, S. (2015). On skewed risks in economic models and experiments.
*Journal of Economic Behavior and Organization, 112*, 85–97.CrossRefGoogle Scholar - Eeckhoudt, L., & Gollier, C. (2005). The impact of prudence on optimal prevention.
*Economic Theory, 26*, 989–994.CrossRefGoogle Scholar - Eeckhoudt, L., Liu, L., & Meyer, J. (2017). Restricted increases in risk aversion and their application.
*Economic Theory, 64*, 161–181.CrossRefGoogle Scholar - Ehrlich, I., & Becker, G. (1972). Market insurance and self-insurance.
*Journal of Political Economy, 80*, 623–648.CrossRefGoogle Scholar - Fu, Q., & Lu, J. (2010). Contest design and optimal endogenous entry.
*Economic Inquiry, 48*, 80–88.CrossRefGoogle Scholar - Gradstein, M., & Konrad, K. A. (1999). Orchestrating rent seeking contests.
*The Economic Journal, 109*, 536–545.CrossRefGoogle Scholar - 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 - Jindapon, P., & Whaley, C. A. (2015). Risk lovers and the rent over-investment puzzle.
*Public Choice, 164*, 87–101.CrossRefGoogle Scholar - Keenan, D. C., & Snow, A. (2016). Strong increases in downside risk aversion.
*Geneva Risk and Insurance Review, 41*, 149–161.CrossRefGoogle Scholar - Konrad, K., & Schlesinger, H. (1997). Risk aversion in rent-seeking and rent-augmenting games.
*The Economic Journal, 107*, 1671–1683.CrossRefGoogle Scholar - Li, J. (2009). Comparative higher-degree Ross risk aversion.
*Insurance: Mathematics and Economics, 45*, 333–336.Google Scholar - 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 - 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 - Liu, L., Rettenmaier, A. J., & Saving, T. R. (2009). Conditional payments and self-protection.
*Journal of Risk and Uncertainty, 38*, 159–172.CrossRefGoogle Scholar - Menegatti, M. (2009). Optimal prevention and prudence in a two-period model.
*Mathematical Social Science, 58*, 393–397.CrossRefGoogle Scholar - Menezes, C. F., Geiss, C., & Tressler, J. (1980). Increasing downside risk.
*American Economic Review, 70*, 921–932.Google Scholar - Modica, S., & Scarsini, M. (2005). A note on comparative downside risk aversion.
*Journal of Economic Theory, 122*, 267–271.CrossRefGoogle Scholar - Moldovanu, B., & Sela, A. (2001). The optimal allocation of prizes in contests.
*American Economic Review, 91*, 542–558.CrossRefGoogle Scholar - Nitzan, S. (1994). Modelling rent-seeking contests.
*European Journal of Political Economy, 10*, 41–60.CrossRefGoogle Scholar - 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 - Pratt, J. (1964). Risk aversion in the small and in the large.
*Econometrica, 32*, 122–136.CrossRefGoogle Scholar - 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 - Rothschild, M., & Stiglitz, J. E. (1970). Increasing risk: I. A definition.
*Journal of Economic Theory, 2*(3), 225–243.CrossRefGoogle Scholar - Sahm, M. (2017). Risk aversion and prudence in contests.
*Economics Bulletin*, 37.*Issue, 2*, 1122–1132.Google Scholar - Schroyen, F., & Treich, N. (2016). The power of money: Wealth effects in contests.
*Games and Economic Behavior, 100*, 46–68.CrossRefGoogle Scholar - Skaperdas, S. (1996). Contest success functions.
*Economic Theory, 7*, 283–290.CrossRefGoogle Scholar - Skaperdas, S., & Gan, L. (1995). Risk aversion in contests.
*The Economic Journal, 105*, 951–962.CrossRefGoogle Scholar - Treich, N. (2010). Risk-aversion and prudence in rent-seeking games.
*Public Choice, 145*, 339–349.CrossRefGoogle Scholar - 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 - Yates, A. J. (2011). Winner-pay contests.
*Public Choice, 147*, 93–106.CrossRefGoogle Scholar