IDEAS home Printed from https://ideas.repec.org/p/haf/huedwp/wp201006.html
   My bibliography  Save this paper

The Optimal Design of Rewards in Contests

Author

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
    as

    Download full text from publisher

    File URL: http://hevra.haifa.ac.il/econ/wp_files/wp201006.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. repec:bla:jindec:v:50:y:2002:i:4:p:417-30 is not listed on IDEAS
    4. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    10. 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.
    11. 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.
    12. 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.
    13. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    14. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    15. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    16. 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.
    17. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sela, Aner, 2016. "Two-stage contests with effort-dependent rewards," CEPR Discussion Papers 11113, C.E.P.R. Discussion Papers.
    2. 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.
    3. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    2. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Aner Sela, 2016. "Two Stage Contests With Effort-Dependent Rewards," Working Papers 1612, Ben-Gurion University of the Negev, Department of Economics.
    4. Stefan Jönsson & Armin Schmutzler, 2013. "All-pay auctions: Implementation and optimality," ECON - Working Papers 108, Department of Economics - University of Zurich.
    5. Subhasish M. Chowdhury, 2017. "The All‐Pay Auction with Nonmonotonic Payoff," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 375-390, October.
    6. David Pérez-Castrillo & David Wettstein, 2012. "Innovation Contests," Working Papers 654, Barcelona School of Economics.
    7. David Perez Castrillo & David Wettstein, 2014. "Discrimination in a new model of contests with two-sided asymmetric information," Working Papers 1407, Ben-Gurion University of the Negev, Department of Economics.
    8. Bettina Klose & Dan Kovenock, 2015. "Extremism drives out moderation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 861-887, April.
    9. Kräkel, Matthias & Szech, Nora & von Bieberstein, Frauke, 2014. "Externalities in recruiting," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PA), pages 123-135.
    10. Kyung Hwan Baik & Jong Hwa Lee, 2013. "Endogenous Timing In Contests With Delegation," Economic Inquiry, Western Economic Association International, vol. 51(4), pages 2044-2055, October.
    11. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Schwartz, Alexandra, 2014. "Lottery versus all-pay auction contests: A revenue dominance theorem," Games and Economic Behavior, Elsevier, vol. 83(C), pages 116-126.
    12. Yizhaq Minchuk & Aner Sela, 2020. "Contests with insurance," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 1-22, June.
    13. David Pérez‐Castrillo & David Wettstein, 2016. "Discrimination In A Model Of Contests With Incomplete Information About Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 881-914, August.
    14. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2019. "A general framework for studying contests," MPRA Paper 97363, University Library of Munich, Germany.
    15. Bettina Klose & Dan Kovenock, 2015. "The all-pay auction with complete information and identity-dependent externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 1-19, May.
    16. 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.
    17. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    18. Toomas Hinnosaar, 2016. "Dynamic common-value contests," Carlo Alberto Notebooks 479, Collegio Carlo Alberto.
    19. Subhasish Chowdhury & Roman Sheremeta, 2015. "Strategically equivalent contests," Theory and Decision, Springer, vol. 78(4), pages 587-601, April.
    20. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.

    More about this item

    Keywords

    contests; innovation; mechanism design;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:haf:huedwp:wp201006. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Anna Rubinchik (email available below). General contact details of provider: https://edirc.repec.org/data/dehaiil.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.