IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v63y2008i2p435-467.html
   My bibliography  Save this article

Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate

Author

Listed:
  • Satterthwaite, Mark
  • Shneyerov, Artyom

Abstract

Consider a decentralized, dynamic market with an infinite horizon and incomplete information in which buyers and sellers' values for the traded good are private and independently drawn. Time is discrete, each period has length [delta], and each unit of time a large number of new buyers and sellers enter the market. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, the seller and winning buyer exit with their realized utility. Traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate. We show that in all steady state, perfect Bayesian equilibria, as [delta] approaches zero, equilibrium prices converge to the Walrasian price and realized allocations converge to the competitive allocation.

Suggested Citation

  • Satterthwaite, Mark & Shneyerov, Artyom, 2008. "Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate," Games and Economic Behavior, Elsevier, vol. 63(2), pages 435-467, July.
  • Handle: RePEc:eee:gamebe:v:63:y:2008:i:2:p:435-467
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00092-4
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    as
    1. Serrano, Roberto, 2002. "Decentralized information and the Walrasian outcome: a pairwise meetings market with private values," Journal of Mathematical Economics, Elsevier, pages 65-89.
    2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    3. Falkinger, Josef, 2007. "Attention economies," Journal of Economic Theory, Elsevier, pages 266-294.
    4. Oliver Hart & John Moore, 2004. "Agreeing Now to Agree Later: Contracts that Rule Out but do not Rule In," ESE Discussion Papers 109, Edinburgh School of Economics, University of Edinburgh.
    5. Mark Satterthwaite & Artyom Shneyerov, 2007. "Dynamic Matching, Two-Sided Incomplete Information, and Participation Costs: Existence and Convergence to Perfect Competition," Econometrica, Econometric Society, pages 155-200.
    6. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "Bilateral matching and bargaining with private information," Games and Economic Behavior, Elsevier, pages 748-762.
    7. Elul, Ronel & Silva-Reus, Jose & Volij, Oscar, 2002. "Will you marry me?: A perspective on the gender gap," Journal of Economic Behavior & Organization, Elsevier, vol. 49(4), pages 549-572, December.
    8. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
    9. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, pages 20-54.
    10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    11. Dean Karlan & Markus M. Möbius & Tanya S. Rosenblat & Adam Szeidl & Hunt Allcott, 2007. "Community Size and Network Closure," American Economic Review, American Economic Association, pages 80-85.
    12. Martin W. Cripps & Jeroen M. Swinkels, 2006. "Efficiency of Large Double Auctions," Econometrica, Econometric Society, pages 47-92.
    13. Gianni De Fraja & Jozsef Sakovics, 2001. "Walras Retrouve: Decentralized Trading Mechanisms and the Competitive Price," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 842-863, August.
    14. Alp E. Atakan, 2010. "Efficient Dynamic Matching with Costly Search," Koç University-TUSIAD Economic Research Forum Working Papers 1030, Koc University-TUSIAD Economic Research Forum.
    15. Philip J Reny & Motty Perry, 2006. "Toward a Strategic Foundation for Rational Expectations Equilibrium," Econometrica, Econometric Society, vol. 74(5), pages 1231-1269, September.
    16. Ascensión Andina-Díaz & Miguel Meléndez-Jiménez, 2009. "Voting in small networks with cross-pressure," Spanish Economic Review, Springer;Spanish Economic Association, vol. 11(2), pages 99-124, June.
    17. Dale T. Mortensen & Randall Wright, 2002. "Competitive Pricing and Efficiency in Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 1-20, February.
    18. Alp E. Atakan, 2010. "Competitive Equilibria in Decentralized Matching with Incomplete Information," Koç University-TUSIAD Economic Research Forum Working Papers 1031, Koc University-TUSIAD Economic Research Forum.
    19. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, Coalitions, and Competition," Economic theory and game theory 014, Nir Dagan, revised May 1999.
    20. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
    21. Hyeok Jeong & Robert Townsend, 2007. "Sources of TFP growth: occupational choice and financial deepening," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(1), pages 179-221, July.
    22. Fudenberg, Drew & Mobius, Markus & Szeidl, Adam, 2007. "Existence of equilibrium in large double auctions," Journal of Economic Theory, Elsevier, pages 550-567.
    23. Tanya S. Rosenblat & Markus M. Mobius, 2004. "Getting Closer or Drifting Apart?," The Quarterly Journal of Economics, Oxford University Press, pages 971-1009.
    24. Falkinger, Josef, 2007. "Attention economies," Journal of Economic Theory, Elsevier, pages 266-294.
    25. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    26. Harvey E. Lapan & David A. Hennessy, 2002. "Symmetry and order in the portfolio allocation problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 747-772.
    27. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    28. Asher Wolinsky, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 71-84.
    29. Shneyerov, Art & Wong, Adam Chi Leung, 2007. "The Rate of Convergence to Perfect Competition of a Simple Matching and Bargaining Mechanism," Microeconomics.ca working papers shneyerov-07-05-01-03-43-, Vancouver School of Economics, revised 01 May 2007.
    30. Acemoglu, Daron & Shimer, Robert, 1997. "Efficient Wage Dispersion," CEPR Discussion Papers 1572, C.E.P.R. Discussion Papers.
    31. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, coalitions and competition," Economics Working Papers 178, Department of Economics and Business, Universitat Pompeu Fabra.
    32. Nir Dagan & Roberto Serrano & Oscar Volij, 2000. "Bargaining, coalitions and competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 279-296.
    33. Mark A. Satterthwaite & Steven R. Williams, 1989. "The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 477-498.
    34. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    35. Mark A. Satterthwaite & Steven R. Williams, 2002. "The Optimality of a Simple Market Mechanism," Econometrica, Econometric Society, vol. 70(5), pages 1841-1863, September.
    36. Wolinsky, Asher, 1990. "Information Revelation in a Market with Pairwise Meetings," Econometrica, Econometric Society, pages 1-23.
    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. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "Bilateral matching and bargaining with private information," Games and Economic Behavior, Elsevier, pages 748-762.
    2. Dipjyoti Majumdar & Artyom Shneyerov & Huan Xie, 2010. "How Optimism Leads to Price Discovery and Efficiency in a Dynamic Matching Market," Working Papers 10004, Concordia University, Department of Economics.
    3. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "The rate of convergence to perfect competition of matching and bargaining mechanisms," Journal of Economic Theory, Elsevier, pages 1164-1187.
    4. Dewan Mostafizur Rahman Author_Email: & Kohinur Akter, 2011. "Financial Liberalization And Interest Rate Convergence-An Empirical Study On Bangladesh," 2nd International Conference on Business and Economic Research (2nd ICBER 2011) Proceeding 2011-456, Conference Master Resources.
    5. Stephan Lauermann & Gábor Virág, 2012. "Auctions in Markets: Common Outside Options and the Continuation Value Effect," American Economic Journal: Microeconomics, American Economic Association, pages 107-130.
    6. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, pages 663-689.
    7. Simon Loertscher & Andras Niedermayer, 2012. "Assessing the Performance of Simple Contracts Empirically:The Case of Percentage Fees," Department of Economics - Working Papers Series 1163, The University of Melbourne.
    8. Lauermann, Stephan, 2012. "Asymmetric information in bilateral trade and in markets: An inversion result," Journal of Economic Theory, Elsevier, pages 1969-1997.
    9. Satterthwaite, Mark A. & Williams, Steven R. & Zachariadis, Konstantinos E., 2014. "Optimality versus practicality in market design: A comparison of two double auctions," Games and Economic Behavior, Elsevier, pages 248-263.
    10. Athey, Susan & Miller, David A., 2007. "Efficiency in repeated trade with hidden valuations," Theoretical Economics, Econometric Society.
    11. Simon Board & Andrzej Skrzypacz, 2016. "Revenue Management with Forward-Looking Buyers," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 1046-1087.
    12. Shneyerov, Artyom, 2014. "A Walrasian Rubinstein and Wolinsky model," Economics Letters, Elsevier, vol. 124(2), pages 314-317.
    13. Shneyerov, Artyom & Wong, Adam Chi Leung, 2011. "The role of private information in dynamic matching and bargaining: Can it be good for efficiency?," Economics Letters, Elsevier, vol. 112(1), pages 128-131, July.
    14. Said, Maher, 2011. "Sequential auctions with randomly arriving buyers," Games and Economic Behavior, Elsevier, vol. 73(1), pages 236-243, September.
    15. Artyom Shneyerov & Adam Chi Leung Won, 2008. "The Rate of Convergence to Perfect Competition of Matching and Bargaining Mechanisms," Discussion Papers 1467, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    More about this item

    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:eee:gamebe:v:63:y:2008:i:2:p:435-467. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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 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 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.