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Private Monitoring in Auctions

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  • Andreas Blume
  • Paul Heidhues

Abstract

We study collusion in repeated first-price auctions under the condition of minimal information release by the auctioneer. In each auction a bidder only learns whether or not he won the object. Bidders do not observe other bidders’ bids, who participates or who wins in case they are not the winner. We show that for large enough discount factors collusion can nevertheless be supported in the infinitely repeated game. While there is a unique Nash equilibrium in public strategies, in which bidders bid competitively in every period, there are simple Nash equilibria in private strategies that support bid rotation. Equilibria that either improve on bid rotation or satisfy the requirement of Bayesian perfection, but not both, are only slightly more complex. Our main result is the construction of perfect Bayesian equilibria that improve on bid rotation. These equilibria require complicated inferences off the equilibrium path. A deviator may not know who has observed his deviation and consequently may have an incentive to use strategic experimentation to learn about the bidding behavior of his rivals. ZUSAMMENFASSUNG - (Privates Monitoring in Auktionen) Der Beitrag untersucht, inwieweit Bieter Kollusion, bzw. stillschweigende Abkommen, in wiederholten Erstpreisauktionen aufrecht erhalten können, in welchen der Auktionator alle Informationen zurückhält. Nach jeder Auktion lernt ein Bieter nur, ob er das Objekt gewonnen hat oder nicht. Ein Bieter kann weder die Gebote der anderen Bieter beobachten, noch kann er beobachten, welche Bieter an der Auktion teilgenommen haben und wer gewonnen hat - solange er nicht selbst das Objekt erhält. Wir zeigen, dass in dem unendlich wiederholten Spiel für hinreichend geduldige Bieter Kollusion möglich ist. Es existiert zwar ein eindeutiges Gleichgewicht in öffentlichen Strategien, in welchem die Bieter in jeder Periode kompetitiv bieten, aber es gibt einfache Nash-Gleichgewichte in privaten Strategien, die Bieterrotation durchsetzen. Wir zeigen auch, dass Bieterrotation das Ergebnis eines perfekt bayesianischen Gleichgewichtes sein kann. Nash-Gleichgewichte, die höhere erwartete Gewinne als Bieterrotation erzielen, sind nur ein wenig komplexer. Das Hauptergebnis ist die Konstruktion von (essentiell) perfekt bayesianischen Gleichgewichten, welche höhere Gewinne als Bieterrotation erzielen. Nach Abweichungen vom Gleichgewichtspfad, müssen die Bieter in diesen Gleichgewichten komplizierte Rückschlüsse auf das Verhalten Ihrer Wettbewerber ziehen. So weiß ein Bieter nach bestimmten Abweichungen nicht, ob diese von seinen Mitspielern beobachtet wurden, und hat ein Interesse daran, durch strategisches experimentieren das Bietverhalten seiner Rivalen kennenzulernen.

Suggested Citation

  • Andreas Blume & Paul Heidhues, 2003. "Private Monitoring in Auctions," CIG Working Papers SP II 2003-14, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
  • Handle: RePEc:wzb:wzebiv:spii2003-14
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    References listed on IDEAS

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    Cited by:

    1. Rachmilevitch, Shiran, 2013. "Endogenous bid rotation in repeated auctions," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1714-1725.
    2. Antonio Miralles, 2010. "Self-enforced collusion through comparative cheap talk in simultaneous auctions with entry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 523-538, March.
    3. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    4. Rachmilevitch, Shiran, 2015. "Bribing in second-price auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 191-205.
    5. Giuseppe Lopomo & Leslie Marx & Peng Sun, 2011. "Bidder collusion at first-price auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 15(3), pages 177-211, September.
    6. Johannes Münster, 2009. "Repeated Contests with Asymmetric Information," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(1), pages 89-118, February.
    7. Rachmilevitch, Shiran, 2014. "First-best collusion without communication," Games and Economic Behavior, Elsevier, vol. 83(C), pages 224-230.
    8. Andreas Blume & April M. Franco & Paul Heidhues, 2011. "Dynamic coordination via organizational routines," ESMT Research Working Papers ESMT-11-10, ESMT European School of Management and Technology.
    9. Chan, Jimmy & Zhang, Wenzhang, 2015. "Collusion enforcement with private information and private monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 188-211.
    10. David A. Miller, 2012. "Robust Collusion with Private Information," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 778-811.
    11. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    12. Igal Milchtaich, 2015. "Polyequilibrium," Working Papers 2015-06, Bar-Ilan University, Department of Economics.
    13. Calzolari, Giacomo & Spagnolo, Giancarlo, 2009. "Relational Contracts and Competitive Screening," CEPR Discussion Papers 7434, C.E.P.R. Discussion Papers.
    14. Rachmilevitch, Shiran, 2013. "Bribing in first-price auctions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 214-228.
    15. Münster, Johannes, 2008. "Repeated contests with asymmetric information
      [Wiederholte Wettkämpfe mit asymmetrischer Information]
      ," Discussion Papers, Research Unit: Market Processes and Governance SP II 2008-08, Social Science Research Center Berlin (WZB).
    16. Leo, Greg, 2017. "Taking turns," Games and Economic Behavior, Elsevier, vol. 102(C), pages 525-547.
    17. Johannes Hörner & Julian Jamison, 2007. "Collusion with (almost) no information," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 804-822, September.

    More about this item

    Keywords

    Itacit collusion; repeated auctions; supergames; contagion; bid-rotation; trigger strategies.;

    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

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