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From Custer to Thermopylae: Last stand behavior in multi-stage contests

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  • Gelder, Alan

Abstract

In a multi-stage contest known as a two-player race, players display two fundamental behaviors: (1) the laggard will make a last stand in order to avoid the cost of losing; and (2) the player who is ahead will defend his lead if it is threatened. Last stand behavior, in particular, contrasts with previous research where the underdog simply gives up. The distinctive results are achieved by introducing losing penalties and discounting into the racing environment. This framework permits the momentum effect, typically ascribed to the winner of early stages, to be more thoroughly examined. I study the likelihood that the underdog will catch up. I find that neck-and-neck races are common when the losing penalty is large relative to the winning prize, while landslide victories occur when the prize is relatively large. Closed-form solutions are given for the case where players have a common winning prize and losing penalty.

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  • Gelder, Alan, 2014. "From Custer to Thermopylae: Last stand behavior in multi-stage contests," Games and Economic Behavior, Elsevier, vol. 87(C), pages 442-466.
  • Handle: RePEc:eee:gamebe:v:87:y:2014:i:c:p:442-466
    DOI: 10.1016/j.geb.2014.06.003
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    as
    1. Sela, Aner, 2011. "Best-of-three all-pay auctions," Economics Letters, Elsevier, vol. 112(1), pages 67-70, July.
    2. Brian Knight & Nathan Schiff, 2010. "Momentum and Social Learning in Presidential Primaries," Journal of Political Economy, University of Chicago Press, vol. 118(6), pages 1110-1150.
    3. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
    4. Nti, Kofi O, 1999. "Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-430, March.
    5. 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.
    6. Konrad, Kai A. & Kovenock, Dan, 2005. "Equilibrium and Efficiency in the Tug-Of-War," Purdue University Economics Working Papers 1177, Purdue University, Department of Economics.
    7. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    8. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
    9. Steven Callander, 2007. "Bandwagons and Momentum in Sequential Voting," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 653-684.
    10. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    11. Strumpf, Koleman S, 2002. "Strategic Competition in Sequential Election Contests," Public Choice, Springer, vol. 111(3-4), pages 377-397, June.
    12. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 193-209.
    13. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    14. Christopher Budd & Christopher Harris & John Vickers, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 543-573.
    15. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
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    Cited by:

    1. Kai A Konrad, 2018. "Budget and Effort Choice in Sequential Colonel Blotto Campaigns," CESifo Economic Studies, CESifo, vol. 64(4), pages 555-576.
    2. Häfner, Samuel, 2017. "A tug-of-war team contest," Games and Economic Behavior, Elsevier, vol. 104(C), pages 372-391.
    3. Klumpp, Tilman & Konrad, Kai A. & Solomon, Adam, 2019. "The dynamics of majoritarian Blotto games," Games and Economic Behavior, Elsevier, vol. 117(C), pages 402-419.
    4. Kimbrough, Erik O. & Laughren, Kevin & Sheremeta, Roman, 2020. "War and conflict in economics: Theories, applications, and recent trends," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 998-1013.
    5. Arne Lauber & Christoph March & Marco Sahm, 2022. "Optimal and Fair Prizing in Sequential Round-Robin Tournaments: Experimental Evidence," CESifo Working Paper Series 9651, CESifo.
    6. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    7. Gelder, Alan & Kovenock, Dan, 2017. "Dynamic behavior and player types in majoritarian multi-battle contests," Games and Economic Behavior, Elsevier, vol. 104(C), pages 444-455.
    8. Samuel Häfner, 2022. "Eternal peace in the tug-of-war?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1057-1101, November.
    9. Doğan, Serhat & Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2018. "Multi-player race," Journal of Economic Behavior & Organization, Elsevier, vol. 149(C), pages 123-136.
    10. Vladimir Petkov, 2023. "Prize formation and sharing in multi-stage contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 259-289, January.
    11. Luo, Zijun & Xie, Xin, 2018. "A Model Of rivalries with endogenous prize and strength," Journal of Economic Behavior & Organization, Elsevier, vol. 152(C), pages 215-223.
    12. Mikhail Drugov & Dmitry Ryvkin, 2020. "Hunting for the discouragement effect in contests," Working Papers w0278, New Economic School (NES).
    13. Haoming Liu & Jingfeng Lu & Alberto Salvo, 2023. "Willingness to fight on: Environmental quality in dynamic contests," RAND Journal of Economics, RAND Corporation, vol. 54(2), pages 189-239, June.
    14. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2021. "Race meets bargaining in product development," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(3), pages 702-709, April.
    15. Klumpp, Tilman, 2021. "Colonel Blotto's Tug of War," Working Papers 2021-3, University of Alberta, Department of Economics.
    16. Clark, Derek J. & Nilssen, Tore, 2018. "Keep on fighting: The dynamics of head starts in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 110(C), pages 258-272.
    17. Peter-J. Jost, 2021. "“The ball is round, the game lasts 90 minutes, everything else is pure theoryâ€," Journal of Sports Economics, , vol. 22(1), pages 27-74, January.
    18. Klumpp, Tilman & Konrad, Kai, 2018. "Sequential Majoritarian Blotto Games," Working Papers 2018-8, University of Alberta, Department of Economics.
    19. Feng, Xin & Lu, Jingfeng, 2018. "How to split the pie: Optimal rewards in dynamic multi-battle competitions," Journal of Public Economics, Elsevier, vol. 160(C), pages 82-95.
    20. Shakun D. Mago & Roman M. Sheremeta, 2017. "Multi‐battle Contests: An Experimental Study," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 407-425, October.
    21. Qiang Fu & Jingfeng Lu, 2020. "On Equilibrium Player Ordering In Dynamic Team Contests," Economic Inquiry, Western Economic Association International, vol. 58(4), pages 1830-1844, October.
    22. Lauber, Arne & March, Christoph & Sahm, Marco, 2023. "Optimal and fair prizing in sequential round-robin tournaments: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 141(C), pages 30-51.

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    More about this item

    Keywords

    Last stand; Dynamic contest; Race; All-pay auction; Winning momentum;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • 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
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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