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Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results

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  • Xiao, Jun

Abstract

This paper studies contests in which three or more players compete for two nonidentical prizes. The players have distinct constant marginal costs of performance or bid, which are commonly known. We show that the contests have a generically unique Nash equilibrium, and it is in mixed strategies. Moreover, we characterize the equilibrium payoffs and strategies in closed form. We also study how the equilibrium payoffs and strategies vary with the prizes. As an application, we numerically compute the optimal allocation of prizes that maximizes the total expected bid of asymmetric players.

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  • Xiao, Jun, 2018. "Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 21-34.
  • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:21-34
    DOI: 10.1016/j.jmateco.2017.10.003
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    References listed on IDEAS

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    1. Jeremy Bulow & Jonathan Levin, 2006. "Matching and Price Competition," American Economic Review, American Economic Association, vol. 96(3), pages 652-668, June.
    2. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    3. Rentschler, Lucas & Turocy, Theodore L., 2016. "Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case," Journal of Economic Theory, Elsevier, vol. 163(C), pages 435-466.
    4. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-651, June.
    5. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    6. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    7. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    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. Todd R. Kaplan & David Wettstein, 2006. "Caps on Political Lobbying: Comment," American Economic Review, American Economic Association, vol. 96(4), pages 1351-1354, September.
    10. 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.
    11. Cohen, Chen & Sela, Aner, 2008. "Allocation of prizes in asymmetric all-pay auctions," European Journal of Political Economy, Elsevier, vol. 24(1), pages 123-132, March.
    12. 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.
    13. Jun Xiao, 2012. "Asymmetric All-Pay Contests with Heterogeneous," Department of Economics - Working Papers Series 1151, The University of Melbourne.
    14. Ghazala Azmat & Marc Möller, 2009. "Competition among contests," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 743-768, December.
    15. Yeon-Koo Che & Ian L. Gale, 2006. "Caps on Political Lobbying: Reply," American Economic Review, American Economic Association, vol. 96(4), pages 1355-1360, September.
    16. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-289, March.
    17. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    18. Szymanski, Stefan & Valletti, Tommaso M., 2005. "Incentive effects of second prizes," European Journal of Political Economy, Elsevier, vol. 21(2), pages 467-481, June.
    19. Parreiras, Sérgio O. & Rubinchik, Anna, 2010. "Contests with three or more heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 68(2), pages 703-715, March.
    20. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
    21. Reut Megidish & Aner Sela, 2013. "Allocation of Prizes in Contests with Participation Constraints," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 22(4), pages 713-727, December.
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    Cited by:

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    2. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.

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    Keywords

    Asymmetric; Contest; Unique;
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