IDEAS home Printed from https://ideas.repec.org/p/xrs/sfbmaa/97-11.html
   My bibliography  Save this paper

A learning approach to auctions

Author

Listed:
  • Hon-Suir, S.

    (Faculty of Industrial Engineering and Management Technion)

  • Monderer, Dov

    (Faculty of Industrial Engineering and Management)

  • Sela, Aner

    (Ben Gurion University)

Abstract

We analyze a repeated first-price auction in which the types of the players are determined before the first round. It is proved that if every player is using either a belief-based learning scheme with bounded recall or a generalized fictitious play learning scheme, then for sufficiently large time, the players' bids are in equilibrium in the one-shot auction in which the types are commonly known.

Suggested Citation

  • Hon-Suir, S. & Monderer, Dov & Sela, Aner, 1997. "A learning approach to auctions," Sonderforschungsbereich 504 Publications 97-11, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  • Handle: RePEc:xrs:sfbmaa:97-11
    Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
    as

    Download full text from publisher

    File URL: http://www.sfb504.uni-mannheim.de/publications/dp97-11.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Thorlund-Petersen, Lars, 1990. "Iterative computation of cournot equilibrium," Games and Economic Behavior, Elsevier, vol. 2(1), pages 61-75, March.
    3. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
    4. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    5. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    6. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    7. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    8. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    9. Robert M. Stark & Michael H. Rothkopf, 1979. "Competitive Bidding: A Comprehensive Bibliography," Operations Research, INFORMS, vol. 27(2), pages 364-390, April.
    10. Paul Milgrom & John Roberts, 2010. "Adaptive and Sophisticated Learning in Repeated Normal-Form Games," Levine's Working Paper Archive 418, David K. Levine.
    11. Laffont, Jean-Jacques, 1997. "Game theory and empirical economics: The case of auction data 1," European Economic Review, Elsevier, vol. 41(1), pages 1-35, January.
    12. Wolfstetter, Elmar, 1996. "Auctions: An Introduction," Journal of Economic Surveys, Wiley Blackwell, vol. 10(4), pages 367-420, December.
    13. Robert B. Wilson, 2021. "Strategic Analysis of Auctions," Econometrica, Econometric Society, vol. 89(2), pages 555-561, March.
    14. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    15. Bikhchandani, Sushil, 1988. "Reputation in repeated second-price auctions," Journal of Economic Theory, Elsevier, vol. 46(1), pages 97-119, October.
    16. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    17. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    18. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-1499, November.
    19. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    20. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    21. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    22. McAfee R. Preston & Vincent Daniel, 1993. "The Declining Price Anomaly," Journal of Economic Theory, Elsevier, vol. 60(1), pages 191-212, June.
    23. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
    24. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    25. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    26. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
    27. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Atanasios Mitropoulos, 2001. "Learning Under Little Information: An Experiment on Mutual Fate Control," Game Theory and Information 0110003, University Library of Munich, Germany.
    2. Xiaotie Deng & Xinyan Hu & Tao Lin & Weiqiang Zheng, 2021. "Nash Convergence of Mean-Based Learning Algorithms in First Price Auctions," Papers 2110.03906, arXiv.org, revised Feb 2023.
    3. Holzman, Ron & Kfir-Dahav, Noa & Monderer, Dov & Tennenholtz, Moshe, 2004. "Bundling equilibrium in combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 47(1), pages 104-123, April.
    4. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    5. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    6. Rene Saran & Roberto Serrano, 2010. "Ex-post regret learning in games with fixed and random matching: The case of private values," Working Papers 2010-11, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    7. Saran, Rene & Serrano, Roberto, 2014. "Ex-post regret heuristics under private values (I): Fixed and random matching," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 97-111.
    8. Krishnamurthy Iyer & Ramesh Johari & Mukund Sundararajan, 2014. "Mean Field Equilibria of Dynamic Auctions with Learning," Management Science, INFORMS, vol. 60(12), pages 2949-2970, December.
    9. Dawid, Herbert, 1999. "On the convergence of genetic learning in a double auction market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1545-1567, September.
    10. Fernando Louge & Frank Riedel, 2012. "Evolutionary Stability in First Price Auctions," Dynamic Games and Applications, Springer, vol. 2(1), pages 110-128, March.
    11. Johannes Horner & Julian Jamison, 2006. "Private Information in Sequential Common-Value Auctions," Discussion Papers 1422, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Mitropoulos, Atanasios, 2001. "Learning under minimal information: An experiment on mutual fate control," Journal of Economic Psychology, Elsevier, vol. 22(4), pages 523-557, August.
    13. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    14. Metzger, Lars Peter, 2014. "Invader strategies in the war of attrition with private information," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 160-166.
    15. Hailu, Atakelty & Schilizzi, Steven & Thoyer, Sophie, 2005. "Assessing the performance of auctions for the allocation of conservation contracts: Theoretical and computational approaches," 2005 Annual meeting, July 24-27, Providence, RI 19478, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    16. Santiago R. Balseiro & Yonatan Gur, 2019. "Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium," Management Science, INFORMS, vol. 65(9), pages 3952-3968, September.
    17. Amy Greenwald & Karthik Kannan & Ramayya Krishnan, 2010. "On Evaluating Information Revelation Policies in Procurement Auctions: A Markov Decision Process Approach," Information Systems Research, INFORMS, vol. 21(1), pages 15-36, March.
    18. Balachander Subramanian & Kannan Karthik & Schwartz David G, 2009. "A Theoretical and Empirical Analysis of Alternate Auction Policies for Search Advertisements," Review of Marketing Science, De Gruyter, vol. 7(1), pages 1-51, December.
    19. Ashish Arora & Amy Greenwald & Karthik Kannan & Ramayya Krishnan, 2007. "Effects of Information-Revelation Policies Under Market-Structure Uncertainty," Management Science, INFORMS, vol. 53(8), pages 1234-1248, August.
    20. Johannes Horner & Julian Jamison, 2003. "Private Information in Repeated Auctions," Levine's Bibliography 666156000000000108, UCLA Department of Economics.
    21. Amir Danak & Shie Mannor, 2012. "Approximately optimal bidding policies for repeated first-price auctions," Annals of Operations Research, Springer, vol. 196(1), pages 189-199, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roberto Burguet, 2000. "Auction theory: a guided tour," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 3-50, January.
    2. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    3. Jean-Jacques Laffont, 1998. "Théorie des jeux et économie empirique : le cas des données issues d'enchères," Économie et Prévision, Programme National Persée, vol. 132(1), pages 121-137.
    4. Laffont, Jean-Jacques, 1997. "Game theory and empirical economics: The case of auction data 1," European Economic Review, Elsevier, vol. 41(1), pages 1-35, January.
    5. Cramton, Peter C, 1995. "Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(2), pages 267-343, Summer.
    6. Lawrence M. Ausubel & Peter Cramton & Marek Pycia & Marzena Rostek & Marek Weretka, 2014. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1366-1400.
    7. Wolfstetter, Elmar, 1998. "Auktionen und Ausschreibungen: Bedeutungen und Grenzen des linkage-Prinzips," SFB 373 Discussion Papers 1998,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. 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.
    9. David Lucking-Reiley, 1999. "Using Field Experiments to Test Equivalence between Auction Formats: Magic on the Internet," American Economic Review, American Economic Association, vol. 89(5), pages 1063-1080, December.
    10. Thomas D. Jeitschko, 1998. "Learning in Sequential Auctions," Southern Economic Journal, John Wiley & Sons, vol. 65(1), pages 98-112, July.
    11. Michel Mougeot & Pierre Malgrange, 2002. "Présentation générale," Économie et Prévision, Programme National Persée, vol. 156(5), pages 1-7.
    12. Emiel Maasland & Sander Onderstal, 2006. "Going, Going, Gone! A Swift Tour of Auction Theory and its Applications," De Economist, Springer, vol. 154(2), pages 197-249, June.
    13. Söllner, Matthias, 2008. "Menschliches Verhalten in elektronischen Märkten," Bayreuth Reports on Information Systems Management 34, University of Bayreuth, Chair of Information Systems Management.
    14. Committee, Nobel Prize, 2020. "Improvements to auction theory and inventions of new auction formats," Nobel Prize in Economics documents 2020-2, Nobel Prize Committee.
    15. Jofre-Bonet, Mireia & Pesendorfer, Martin, 2014. "Optimal sequential auctions," International Journal of Industrial Organization, Elsevier, vol. 33(C), pages 61-71.
    16. J. Reiß & Jens Schöndube, 2010. "First-price equilibrium and revenue equivalence in a sequential procurement auction model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 99-141, April.
    17. Atanu R. Sinha & Eric A. Greenleaf, 2000. "The Impact of Discrete Bidding and Bidder Aggressiveness on Sellers' Strategies in Open English Auctions: Reserves and Covert Shilling," Marketing Science, INFORMS, vol. 19(3), pages 244-265, May.
    18. R. Preston McAfee & John McMillan, 1996. "Analyzing the Airwaves Auction," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 159-175, Winter.
    19. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    20. Peter Cramton, 1997. "The FCC Spectrum Auctions: An Early Assessment," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(3), pages 431-495, September.

    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    Corrections

    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:xrs:sfbmaa:97-11. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Carsten Schmidt (email available below). General contact details of provider: https://edirc.repec.org/data/sfmande.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.