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Monotone Equilibrium in Multi-Unit Auctions

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  • David McAdams

Abstract

In two-sided multi-unit auctions having a variety of payment rules, including uniform-price and discriminatory auctions, a monotone pure-strategy equilibrium (MPSE) exists when bidders are risk neutral with independent multi-dimensional types and interdependent values. In fact, all mixed-strategy equilibria are ex post allocation and interim expected payment equivalent to MPSE. Thus, for standard expected surplus/revenue analysis, there is no loss restricting attention to monotone strategies. Copyright 2006, Wiley-Blackwell.

Suggested Citation

  • David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1039-1056.
  • Handle: RePEc:oup:restud:v:73:y:2006:i:4:p:1039-1056
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    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2006.00407.x
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    Cited by:

    1. Bogetoft, Peter & Nielsen, Kurt, 2003. "Yardstick Based Procurement Design In Natural Resource Management," 2003 Annual Meeting, August 16-22, 2003, Durban, South Africa 25910, International Association of Agricultural Economists.
    2. McAdams, David, 2002. "Bidding Lower with Higher Values in Multi-Object Auction," Working papers 4249-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Papakonstantinou, Athanasios & Bogetoft, Peter, 2017. "Multi-dimensional procurement auction under uncertain and asymmetric information," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1171-1180.
    4. Manzano, Carolina & Vives, Xavier, 2016. "Market Power and Welfare in Asymmetric Divisible Good Auctions," CEPR Discussion Papers 11731, C.E.P.R. Discussion Papers.
    5. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    6. Kastl, Jakub, 2012. "On the properties of equilibria in private value divisible good auctions with constrained bidding," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 339-352.
    7. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    8. Bresky, Michal, 2013. "Revenue and efficiency in multi-unit uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 82(C), pages 205-217.
    9. McAdams, David, 2008. "Partial identification and testable restrictions in multi-unit auctions," Journal of Econometrics, Elsevier, vol. 146(1), pages 74-85, September.
    10. Han, Seungjin, 2013. "Asymmetric first-price menu auctions under intricate uncertainty," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2068-2095.
    11. Olivier Armantier & Jean-Pierre Florens & Jean-Francois Richard, 2008. "Approximation of Nash equilibria in Bayesian games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 965-981.
    12. repec:eee:indorg:v:54:y:2017:i:c:p:125-147 is not listed on IDEAS
    13. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    14. McAdams, David, 2007. "On the failure of monotonicity in uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 137(1), pages 729-732, November.
    15. Barelli, Paulo & Duggan, John, 2015. "Purification of Bayes Nash equilibrium with correlated types and interdependent payoffs," Games and Economic Behavior, Elsevier, vol. 94(C), pages 1-14.
    16. John Roberts, 2008. "Susan C. Athey: John Bates Clark Award Winner 2007," Journal of Economic Perspectives, American Economic Association, vol. 22(4), pages 181-198, Fall.
    17. Michal Bresky, 2008. "Pure Equilibrium Strategies in Multi-unit Auctions with Private Value Bidders," CERGE-EI Working Papers wp376, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    18. Paulo Barelli & John Duggan, 2011. "Extremal Choice Equilibrium: Existence and Purification with Infinite-Dimensional Externalities," RCER Working Papers 567, University of Rochester - Center for Economic Research (RCER).
    19. Ennio Bilancini & Leonardo Boncinelli, 2016. "Strict Nash equilibria in non-atomic games with strict single crossing in players (or types) and actions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 95-109, April.
    20. Galavotti, Stefano, 2009. "Bilateral trade with apositional traders," Research in Economics, Elsevier, vol. 63(3), pages 172-188, September.

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