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The Optimal Design of Rewards in Contests

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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 & Wettstein, David, "undated". "The Optimal Design of Rewards in Contests," Working Papers WP2010/6, University of Haifa, Department of Economics, revised 22 Nov 2010.
  • Handle: RePEc:haf:huedwp:wp201006
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    References listed on IDEAS

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    1. Oliver Hart & John Moore, 1985. "Incomplete Contracts and Renegotiation," Working papers 367, Massachusetts Institute of Technology (MIT), Department of Economics.
    2. McAfee, R. Preston & McMillan, John, 1989. "Government procurement and international trade," Journal of International Economics, Elsevier, pages 291-308.
    3. Frondel, Manuel & Ritter, Nolan & Schmidt, Christoph M. & Vance, Colin, 2010. "Economic impacts from the promotion of renewable energy technologies: The German experience," Energy Policy, Elsevier, pages 4048-4056.
    4. Kaplan, Todd, et al, 2002. "All-Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    5. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    6. Hart, Oliver D & Moore, John, 1988. "Incomplete Contracts and Renegotiation," Econometrica, Econometric Society, pages 755-785.
    7. Michael R. Baye & Dan Kovenock & Casper G. de Vries, 2009. "Contests with Rank-Order Spillovers," Tinbergen Institute Discussion Papers 09-066/2, Tinbergen Institute.
    8. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, pages 646-671.
    9. 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.
    10. 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), pages 291-305.
    11. 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), pages 291-305.
    12. Michael Baye & Dan Kovenock & Casper Vries, 2012. "Contests with rank-order spillovers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 315-350.
    13. Fu, Qiang & Lu, Jingfeng & Lu, Yuanzhu, 2012. "Incentivizing R&D: Prize or subsidies?," International Journal of Industrial Organization, Elsevier, pages 67-79.
    14. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, pages 1111-1133.
    15. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, pages 434-451.
    16. Kaplan, T.R. & Luski, I. & Wettstein, D., 2000. "Innovative Activity and Sunk Cost," Discussion Papers 0006, Exeter University, Department of Economics.
    17. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, pages 1111-1133.
    18. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, pages 2230-2260.
    19. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    20. Michael Baye & Dan Kovenock & Casper Vries, 2012. "Contests with rank-order spillovers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 315-350.
    21. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
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    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:spr:reecde:v:21:y:2017:i:4:d:10.1007_s10058-017-0205-9 is not listed on IDEAS
    3. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Paper Series dp662, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    5. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    6. Sela, Aner, 2016. "Two-stage contests with effort-dependent rewards," CEPR Discussion Papers 11113, C.E.P.R. Discussion Papers.
    7. Fu, Qiang & Lu, Jingfeng & Lu, Yuanzhu, 2012. "Incentivizing R&D: Prize or subsidies?," International Journal of Industrial Organization, Elsevier, pages 67-79.

    More about this item

    Keywords

    contests; innovation; mechanism design;

    JEL classification:

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

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