IDEAS home Printed from
   My bibliography  Save this article

Monotone Equilibrium in Multi-Unit Auctions


  • David McAdams


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

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Brander, James & Krugman, Paul, 1983. "A 'reciprocal dumping' model of international trade," Journal of International Economics, Elsevier, vol. 15(3-4), pages 313-321, November.
    2. Marcus Asplund & Volker Nocke, 2006. "Firm Turnover in Imperfectly Competitive Markets -super-1," Review of Economic Studies, Oxford University Press, vol. 73(2), pages 295-327.
    3. Thomas J. Holmes & John J. Stevens, 2004. "Geographic concentration and establishment size: analysis in an alternative economic geography model," Journal of Economic Geography, Oxford University Press, vol. 4(3), pages 227-250, June.
    4. DEL GATTO, Massimo & MION, Giordano & OTTAVIANO, Gianmarco I.P., 2006. "Trade integration, firm selection and the costs of non-Europe," CORE Discussion Papers 2006061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Pierre‐Philippe Combes & Gilles Duranton & Laurent Gobillon & Diego Puga & Sébastien Roux, 2012. "The Productivity Advantages of Large Cities: Distinguishing Agglomeration From Firm Selection," Econometrica, Econometric Society, vol. 80(6), pages 2543-2594, November.
    6. Bernard, Andrew B. & Bradford Jensen, J., 1999. "Exceptional exporter performance: cause, effect, or both?," Journal of International Economics, Elsevier, vol. 47(1), pages 1-25, February.
    7. Nina Pavcnik, 2002. "Trade Liberalization, Exit, and Productivity Improvements: Evidence from Chilean Plants," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 245-276.
    8. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    9. Sofronis K. Clerides & Saul Lach & James R. Tybout, 1998. "Is Learning by Exporting Important? Micro-Dynamic Evidence from Colombia, Mexico, and Morocco," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 903-947.
    10. Gianmarco Ottaviano & Takatoshi Tabuchi & Jacques-FranÁois Thisse, 2002. "Agglomeration and Trade Revisited," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 409-436, May.
    11. repec:rus:hseeco:122439 is not listed on IDEAS
    12. Aw, Bee Yan & Chung, Sukkyun & Roberts, Mark J, 2000. "Productivity and Turnover in the Export Market: Micro-level Evidence from the Republic of Korea and Taiwan (China)," World Bank Economic Review, World Bank Group, vol. 14(1), pages 65-90, January.
    13. Weinstein, David E., 1992. "Competition and unilateral dumping," Journal of International Economics, Elsevier, vol. 32(3-4), pages 379-388, May.
    14. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 441-487.
    15. Jeffrey R. Campbell & Hugo A. Hopenhayn, 2005. "Market Size Matters," Journal of Industrial Economics, Wiley Blackwell, vol. 53(1), pages 1-25, March.
    16. Venables, Anthony J., 1985. "Trade and trade policy with imperfect competition: The case of identical products and free entry," Journal of International Economics, Elsevier, vol. 19(1-2), pages 1-19, August.
    17. Chad Syverson, 2004. "Market Structure and Productivity: A Concrete Example," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1181-1222, December.
    18. Venables, Anthony J, 1987. "Trade and Trade Policy with Differentiated Products: A Chamberlinian-Ricardian Model," Economic Journal, Royal Economic Society, vol. 97(387), pages 700-717, September.
    19. Marcus Asplund & Volker Nocke, 2003. "Firm Turnover in Imperfectly Competitive Markets," PIER Working Paper Archive 03-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    20. Markusen, James R., 1981. "Trade and the gains from trade with imperfect competition," Journal of International Economics, Elsevier, vol. 11(4), pages 531-551, November.
    21. Horstmann, Ignatius J. & Markusen, James R., 1986. "Up the average cost curve: Inefficient entry and the new protectionism," Journal of International Economics, Elsevier, vol. 20(3-4), pages 225-247, May.
    22. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2006. "Trading Partners and Trading Volumes," DEGIT Conference Papers c011_022, DEGIT, Dynamics, Economic Growth, and International Trade.
    23. Feenstra, Robert & Markusen, James R. & Rose, Andrew K, 1998. "Understanding the Home Market Effect and the Gravity Equation: The Role of Differentiating Goods," CEPR Discussion Papers 2035, C.E.P.R. Discussion Papers.
    24. Bernard, Andrew B. & Jensen, J. Bradford & Schott, Peter K., 2006. "Trade costs, firms and productivity," Journal of Monetary Economics, Elsevier, vol. 53(5), pages 917-937, July.
    25. Krugman, Paul R., 1979. "Increasing returns, monopolistic competition, and international trade," Journal of International Economics, Elsevier, vol. 9(4), pages 469-479, November.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:restud:v:73:y:2006:i:4:p:1039-1056. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.