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Second price all-pay auctions, how much money do players get or lose?

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  • Gisèle Umbhauer

Abstract

The paper studies second price all-pay auctions - wars of attrition - in a new way, based on class room experiments and Kosfeld, Droste and Voorneveld’s (2002) best reply matching equilibrium. Two players fight over a prize of value V, have a budget M, submit bids lower or equal to M; both pay the lowest bid and the prize goes to the highest bidder. The behaviour probability distributions in the class room experiments are strikingly different from the mixed Nash equilibrium. They fit with best reply matching or generalized best reply matching, an ordinal logic according to which, if bid A is the best response to bid B, and if B is played with probability p, then A is also played with probability p. In the mixed Nash equilibrium, the expected payoff is never negative and close to 0. In the best reply and generalized best reply matching equilibria, players may lose money, up to 1/12th of the budget when M is large in comparison to V, but they can also get a lot of money, especially if V is large. The study leads to examine possible bifurcations in the bidding behaviour and gives some insights into how to regulate games to avoid pathological gambling with a huge waste of money.

Suggested Citation

  • Gisèle Umbhauer, 2017. "Second price all-pay auctions, how much money do players get or lose?," Working Papers of BETA 2017-16, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2017-16
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    File URL: http://www.beta-umr7522.fr/productions/publications/2017/2017-16.pdf
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    References listed on IDEAS

    as
    1. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    2. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    3. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    4. Lugovskyy, Volodymyr & Puzzello, Daniela & Tucker, Steven, 2010. "An experimental investigation of overdissipation in the all pay auction," European Economic Review, Elsevier, vol. 54(8), pages 974-997, November.
    5. Gisèle Umbhauer, 2017. "Equilibria in discrete and continuous second price all-pay auctions, convergence or yoyo phenomena," Working Papers of BETA 2017-14, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    6. Gneezy, Uri & Smorodinsky, Rann, 2006. "All-pay auctions--an experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 61(2), pages 255-275, October.
    7. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    8. Kosfeld, Michael & Droste, Edward & Voorneveld, Mark, 2002. "A myopic adjustment process leading to best-reply matching," Games and Economic Behavior, Elsevier, vol. 40(2), pages 270-298, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    second price all-pay auction; war of attrition; best reply matching; Nash equilibrium; classroom experiment.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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