## Abstract

In this paper, we first characterize the class of contest success functions (CSFs) that yield contests with equilibria in dominant strategies. Then we study the optimal contest as a decision problem under uncertainty. We consider the classical criteria of Wald, Laplace, Hurwicz and Savage. We find that the CSF that maximizes aggregate effort under these criteria has the form of an additively separable cutoff CSF.

## Keywords

Contests Dominant strategies Optimality under uncertainty Additively separable CSF## JEL classification

C7 D7## Notes

### Acknowledgements

We are grateful to Z. Méder, S. Heinsalu, N. Kudryashova, J. Rueda-Llano, H. Sabourian, B. Schipper, the associate editor and four anonymous referees for very helpful comments. Thanks to the MOMA network under the project ECO2014-57673-REDT for financial support. The first author acknowledges financial support from ECO2014 53051, SGR2014-515 and PROMETEO/2013/037. The second author acknowledges financial support from ECO2014_57442_P, ECO2017_87769_P, MDM 2014-0431 and S2015/HUM-3444.

## References

- Barberá, S., Pattanaik, P.: Falmagne and the rationalizability of stochastic choices in terms of random orderings. Econometrica
**54**, 707–715 (1986)CrossRefGoogle Scholar - Bergemann, D., Schlag, K.: Robust monopoly pricing. J. Econ. Theory
**146**, 2527–2543 (2011)CrossRefGoogle Scholar - Bergemann, D., Morris, S.: Robust Mechanism Design: The Role of Private Information and Higher Order Beliefs, vol. 8318. World Scientific Publishing, Singapore (2012)CrossRefGoogle Scholar
- Bossert, W., Pattanaik, P.K., Xu, Y.: Choice under complete uncertainty: axiomatic characterizations of some decision rules. Econ. Theory
**16**, 295–312 (2000). https://doi.org/10.1007/PL00004080 CrossRefGoogle Scholar - Chawla, S., Hartline, jD, Sivan, B.: Optimal crowdsourcing contests. Games Econ. Behav.
**113**, 80–96 (2019)CrossRefGoogle Scholar - Corchon, L., Ortuño-Ortin, I.: Robust implementation under alternative information structures. Econ. Des.
**1**, 159–171 (1994)Google Scholar - Cubel, M., Sanchez-Pages, S.: An axiomatization of difference-form contest success functions. J. Econ. Behav. Organ.
**131**, 92–105 (2016)CrossRefGoogle Scholar - Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a nash equilibrium. SIAM J. Comput.
**39**, 195–259 (2009)CrossRefGoogle Scholar - Dechenaux, E., Kovenock, D., Sheremeta, R.: A survey of experimental research on contests, all-pay auctions and tournaments. Exp. Econ.
**18**, 609–669 (2015)CrossRefGoogle Scholar - Gill, D., Prowse, V.: A structural analysis of disappointment aversion in real effort competion. Am. Econ. Rev.
**102**, 469–503 (2012)CrossRefGoogle Scholar - Jia, H., Skaperdas, S., Vaidya, S.: Contest functions: theoretical foundations and issues in estimation. Int. J. Ind. Organ.
**31**, 211–22 (2013)CrossRefGoogle Scholar - Laffont, J.J., Maskin, E.: A differential approach to dominant strategy mechanisms. Econometrica
**48**, 1507–1520 (1980)CrossRefGoogle Scholar - Maskin, E., Sjöström, T.: Implementation theory. In: Arrow, K., Sen, A., Suzumura, K. (eds.) Handbook of Social Choice Theory, vol. I, pp. 237–288. Elsevier, Amsterdam (2002)Google Scholar
- Milnor, J.: Games against nature. In: Thrall, R., Coombs, C., Davis, R. (eds.) Decision Processes, pp. 49–61. Wiley, New York (1954)Google Scholar
- Myerson, R.: Optimal auction design. Math. Oper. Res.
**6**, 58–73 (1981)CrossRefGoogle Scholar - Myerson, R.: Mechanism design by an informed principal. Econometrica
**51**, 1767–1797 (1983)CrossRefGoogle Scholar - Polishchuk, L., Tonis, A.: Endogenous contest success functions: a mechanism design approach. Econ. Theory
**52**, 271–297 (2013). https://doi.org/10.1007/s00199-011-0622-x CrossRefGoogle Scholar - Renou, L., Schlag, K.: Minimax regret and strategic uncertainty. J. Econ. Theory
**145**, 264–286 (2010)CrossRefGoogle Scholar - Rezai, A., van der Ploeg, F.: Climate policies under climate model uncertainty: max–min and min–max regret uncertainty. Energy Econ.
**68**, 4–16 (2017)CrossRefGoogle Scholar - Serena, M.: Quality contests. Eur. J. Polit. Econ.
**46**, 15–25 (2017)CrossRefGoogle Scholar - Skaperdas, S., Vaidya, S.: Persuasion as a contest. Econ. Theory
**51**, 465–486 (2012). https://doi.org/10.1007/s00199-009-0497-2 CrossRefGoogle Scholar - Skaperdas, S., Toukanb, A., Vaidya, S.: Difference-form Persuasion contests. J. Public Econ. Theory
**18**, 882–909 (2016)CrossRefGoogle Scholar - Wilson, R.: Game-theoretic approaches to trading processes. In: Bewley, T. (ed.) Advances in Economic Theory: Fifth World Congress, pp. 33–77. Cambridge University Press, Cambridge (1987)CrossRefGoogle Scholar