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Asymmetric Contests with Conditional Investments


  • Ron Siegel


This paper studies equilibrium behavior in a class of games that models asymmetric competitions with unconditional and conditional investments. Such competitions include lobbying settings, labor-market tournaments, and R& races, among others. I provide an algorithm that constructs the unique equilibrium in these games and apply it to study competitions in which a fraction of each competitor's investment is sunk and the rest is paid only by the winners. Complete-information all-pay auctions are a special case. (JEL D44, D72, D82)

Suggested Citation

  • Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
  • Handle: RePEc:aea:aecrev:v:100:y:2010:i:5:p:2230-60

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    References listed on IDEAS

    1. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-294, March.
    2. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    3. Daniele Condorelli, 2009. "What money can't buy: allocations with priority lists, lotteries and queues," Discussion Papers 1482, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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.
    5. 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.
    6. Ellingsen, Tore, 1991. "Strategic Buyers and the Social Cost of Monopoly," American Economic Review, American Economic Association, vol. 81(3), pages 648-657, June.
    7. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    8. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
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    Cited by:

    1. Olivier Bos & Martin Ranger, 2014. "All-Pay Auctions with Polynomial Rewards," Annals of Economics and Statistics, GENES, issue 115-116, pages 361-377.
    2. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    3. Christian Ewerhart, 2014. "Elastic contests and the robustness of the all-pay auctions," ECON - Working Papers 155, Department of Economics - University of Zurich.
    4. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Schwartz, 2012. "Lottery versus All-Pay Auction Contests – A Revenue Dominance Theorem," Ruhr Economic Papers 0315, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    5. Todd Kaplan & David Wettstein, 2015. "The optimal design of rewards in contests," Review of Economic Design, Springer;Society for Economic Design, vol. 19(4), pages 327-339, December.
    6. 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.
    7. 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.
    8. Siegel, Ron, 2014. "Asymmetric all-pay auctions with interdependent valuations," Journal of Economic Theory, Elsevier, vol. 153(C), pages 684-702.
    9. 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.
    10. 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.
    11. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
    12. Jönsson, Stefan & Schmutzler, Armin, 2013. "All-Pay Auctions: Implementation and Optimality," CEPR Discussion Papers 9323, C.E.P.R. Discussion Papers.
    13. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    14. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    15. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    16. Julio González-Díaz & Ron Siegel, 2013. "Matching and price competition: beyond symmetric linear costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 835-844, November.
    17. Ron Siegel, 2014. "Contests with productive effort," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 515-523, August.
    18. Szech, Nora & Weinschenk, Philipp, 2013. "Rebates in a Bertrand game," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 124-133.
    19. 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.
    20. Kräkel, Matthias & Szech, Nora & von Bieberstein, Frauke, 2014. "Externalities in recruiting," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PA), pages 123-135.
    21. 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.
    22. David Pérez-Castrillo & David Wettstein, 2012. "Innovation Contests," Working Papers 654, Barcelona Graduate School of Economics.
    23. Zhiguo He & Gregor Matvos, 2012. "Debt and Creative Destruction: Why Could Subsidizing Corporate Debt be Optimal?," NBER Working Papers 17920, National Bureau of Economic Research, Inc.
    24. repec:zbw:rwirep:0315 is not listed on IDEAS

    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design


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