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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. 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, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    8. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    9. 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.
    10. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Väth, 2009. "Effort Maximization in Asymmetric N-Person Contest Games," CESifo Working Paper Series 2744, CESifo.
    11. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    12. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Schwartz, 2013. "Effort maximization in asymmetric contest games with heterogeneous contestants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 589-630, March.
    13. Hart, Oliver D & Moore, John, 1988. "Incomplete Contracts and Renegotiation," Econometrica, Econometric Society, vol. 56(4), pages 755-785, July.
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    15. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    16. 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.
    17. 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. Sela, Aner, 2016. "Two-stage contests with effort-dependent rewards," CEPR Discussion Papers 11113, C.E.P.R. Discussion Papers.
    2. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    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.

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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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