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The optimal design of rewards in contests

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  • Kaplan, Todd R
  • Wettstein, David

Abstract

Using contests to generate innovation has and is widely used. Such contests often involve offering a prize that depends upon the accomplishment (effort). Using an all-pay auction as a model of a contest, we determine the optimal reward for inducing innovation. In a symmetric environment, we find that the reward should be set to c(x)/c′(x) where c is the cost of producing an innovation of level x. In an asymmetric environment with two firms, we find that it is optimal to set different rewards for each firm. There are cases where this can be replicated by a single reward that depends upon accomplishments of both contestants.

Suggested Citation

  • Kaplan, Todd R & Wettstein, David, 2010. "The optimal design of rewards in contests," MPRA Paper 27397, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:27397
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    References listed on IDEAS

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    1. Hart, Oliver D & Moore, John, 1988. "Incomplete Contracts and Renegotiation," Econometrica, Econometric Society, vol. 56(4), pages 755-785, July.
    2. McAfee, R. Preston & McMillan, John, 1989. "Government procurement and international trade," Journal of International Economics, Elsevier, vol. 26(3-4), pages 291-308, May.
    3. Kaplan, Todd, et al, 2002. "All-Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    4. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    5. Michael Baye & Dan Kovenock & Casper Vries, 2012. "Contests with rank-order spillovers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 315-350, October.
    6. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Väth, Alexandra, 2009. "Effort Maximization in Asymmetric N-person Contest Games," Ruhr Economic Papers 130, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    7. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 434-451, June.
    8. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    9. 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.
    10. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
    11. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    12. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    13. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    14. Todd Kaplan & Israel Luski & Aner Sela & David Wettstein, 2002. "All–Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    15. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
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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. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, University of Exeter, Department of Economics.
    3. 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.
    4. Aner Sela, 2017. "Two-stage contests with effort-dependent values of winning," Review of Economic Design, Springer;Society for Economic Design, vol. 21(4), pages 253-272, December.
    5. Sela, Aner, 2016. "Two-stage contests with effort-dependent rewards," CEPR Discussion Papers 11113, C.E.P.R. Discussion Papers.
    6. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.

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    More about this item

    Keywords

    contests; innovation; mechanism design.;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies

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