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Optimal Rewards in Contests

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  • Cohen, Chen
  • Kaplan, Todd
  • Sela, Aner

Abstract

We study all-pay contests under incomplete information where the reward is a function of the contestant's type and effort. We analyse the optimal reward for the designer when the reward is either multiplicatively separable or additively separable in effort and type. In the multiplicatively separable environment the optimal reward is always positive while in the additively separable environment it may also be negative. In both environments, depending on the designer's utility, the optimal reward may either increase or decrease in the contestants' effort. Finally, in both environments, the designer's payoff depends only upon the expected value of the effort-dependent rewards and not the number of rewards.

Suggested Citation

  • Cohen, Chen & Kaplan, Todd & Sela, Aner, 2004. "Optimal Rewards in Contests," CEPR Discussion Papers 4704, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:4704
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    References listed on IDEAS

    as
    1. Kaplan, Todd, et al, 2002. "All-Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    2. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    3. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-294, March.
    4. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-651, June.
    5. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    6. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-890, September.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Aner Sela, 2016. "Two Stage Contests With Effort-Dependent Rewards," Working Papers 1612, Ben-Gurion University of the Negev, Department of Economics.
    2. repec:eee:jeborg:v:139:y:2017:i:c:p:32-48 is not listed on IDEAS
    3. Hoffmann, Magnus & Rota-Graziosi, Grégoire, 2012. "Endogenous timing in general rent-seeking and conflict models," Games and Economic Behavior, Elsevier, vol. 75(1), pages 168-184.
    4. Stefan Jönsson & Armin Schmutzler, 2013. "All-pay auctions: Implementation and optimality," ECON - Working Papers 108, Department of Economics - University of Zurich.
    5. BOS, Olivier & RANGER, Martin, 2009. "All-pay auctions with endogenous rewards," CORE Discussion Papers 2009059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    7. Sela, Aner, 2008. "Sequential Two-Prize Contests," CEPR Discussion Papers 6769, C.E.P.R. Discussion Papers.
    8. Todd Kaplan & David Wettstein, 2015. "The optimal design of rewards in contests," Review of Economic Design, Springer;Society for Economic Design, vol. 19(4), pages 327-339, December.
    9. Reut Megidish & Aner Sela, 2014. "Caps In Sequential Contests," Economic Inquiry, Western Economic Association International, vol. 52(2), pages 608-617, April.
    10. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    11. Ron Siegel, 2014. "Contests with productive effort," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 515-523, August.
    12. Olivier Bos & Martin Ranger, 2014. "All-Pay Auctions with Polynomial Rewards," Annals of Economics and Statistics, GENES, issue 115-116, pages 361-377.
    13. Ghazala Azmat & Marc Möller, 2009. "Competition among contests," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 743-768.
    14. Alex Gershkov & Jianpei Li & Paul Schweinzer, 2009. "Efficient tournaments within teams," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 103-119.
    15. Aner Sela, 2008. "Sequential Two-Prize Contests," Working Papers 0803, Ben-Gurion University of the Negev, Department of Economics.
    16. Sela, Aner, 2016. "Two-stage contests with effort-dependent rewards," CEPR Discussion Papers 11113, C.E.P.R. Discussion Papers.
    17. Brueggemann, Julia & Meub, Lukas, 2015. "Experimental evidence on the effects of innovation contests," Center for European, Governance and Economic Development Research Discussion Papers 251, University of Goettingen, Department of Economics.
    18. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    19. Fu, Qiang & Lu, Jingfeng & Lu, Yuanzhu, 2012. "Incentivizing R&D: Prize or subsidies?," International Journal of Industrial Organization, Elsevier, vol. 30(1), pages 67-79.
    20. repec:eee:iepoli:v:39:y:2017:i:c:p:72-83 is not listed on IDEAS
    21. Gershkov, Alex & Li, Jianpei & Schweinzer, Paul, 2006. "Collective Production and Incentives," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 186, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    22. Serena, Marco, 2017. "Quality contests," European Journal of Political Economy, Elsevier, vol. 46(C), pages 15-25.

    More about this item

    Keywords

    all-pay auctions; contests; optimal design;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives

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