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It's not always best to be first

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  • Sela, Aner

Abstract

We study a model with n agents, each of whom has both a linear reward function that increases in the agent's effort and an effort constraint. However, since the effort (output) of the players has a negative effect on society the designer imposes a punishment such that the agent with the highest effort who caused the greatest damage is punished. We analyze the equilibrium of this model with either symmetric or asymmetric agents. At all the equilibrium points, all the agents are active and all have positive expected payoffs. We characterize the properties of the agents' equilibrium strategies and compare them to the well-known equilibrium strategies of the all-pay auction in which the agent with the highest effort wins a prize.

Suggested Citation

  • Sela, Aner, 2018. "It's not always best to be first," CEPR Discussion Papers 12887, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:12887
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
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    7. 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.
    8. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
    9. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    10. Benny Moldovanu & Aner Sela & Xianwen Shi, 2012. "Carrots And Sticks: Prizes And Punishments In Contests," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 453-462, April.
    11. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    12. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
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    14. Kagel, John H. & Levin, Dan, 1986. "The Winner's Curse and Public Information in Common Value Auctions," American Economic Review, American Economic Association, vol. 76(5), pages 894-920, December.
    15. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    16. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    17. Thaler, Richard H, 1988. "Anomalies: The Winner's Curse," Journal of Economic Perspectives, American Economic Association, vol. 2(1), pages 191-202, Winter.
    18. Bajari, Patrick & Hortacsu, Ali, 2003. "The Winner's Curse, Reserve Prices, and Endogenous Entry: Empirical Insights from eBay Auctions," RAND Journal of Economics, The RAND Corporation, vol. 34(2), pages 329-355, Summer.
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    Keywords

    Contests; Winner's curse;

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