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The Rate of Convergence to Perfect Competition of a Simple Matching and Bargaining Mechanism

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Author Info
Shneyerov, Art
Wong, Adam Chi Leung

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Abstract

We study the steady-state of a market with inflowing cohorts of buyers and sellers who are randomly matched pairwise and bargain under private information. Two bargaining protocols are considered: take-it-or-leave-it offering and the double auction. There are frictions due to costly search and time discounting, parameterized by a single number t > 0 proportional to the waiting time until the next meeting. We study the efficiency of these mechanisms as the frictions are removed, i.e. t 0. We find that all equilibria of the take-it-or-leave-it offering mechanism converge to the Walrasian limit, at the fastest possible rate O(t) among all bargaining mechanisms. For the double auction mechanism, we find that there are equilibria that converge at the linear rate, those that converge at a slower rate or even not converge at all.

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Publisher Info
Paper provided by Microeconomics.ca Website in its series Micro Theory Working Papers with number shneyerov-07-05-01-03-43-25.

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Length: 31 pages
Date of creation: 01 May 2007
Date of revision: 01 May 2007
Handle: RePEc:ubc:pmicro:shneyerov-07-05-01-03-43-25

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Related research
Keywords: Matching and Bargaining; Search; Double Auctions; Foundations for Perfect Competition; Rate of Convergence;

Other versions of this item:

Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Blouin, Max R & Serrano, Roberto, 2001. "A Decentralized Market with Common Values Uncertainty: Non-Steady States," Review of Economic Studies, Blackwell Publishing, vol. 68(2), pages 323-46, April.
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  2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March. [Downloadable!] (restricted)
  3. Williams, Steven R, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," Review of Economic Studies, Blackwell Publishing, vol. 58(2), pages 351-74, April. [Downloadable!] (restricted)
  4. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July. [Downloadable!] (restricted)
  5. Satterthwaite, Mark A & Williams, Steven R, 1989. "The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large," Review of Economic Studies, Blackwell Publishing, vol. 56(4), pages 477-98, October. [Downloadable!] (restricted)
  6. Martin W Cripps & Jeroen M Swinkels, 2003. "Efficiency of Large Double Auctions," Levine's Working Paper Archive 666156000000000329, David K. Levine. [Downloadable!]
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  7. 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. [Downloadable!] (restricted)
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  8. Mark Satterthwaite & Artyom Shneyerov, 2007. "Dynamic Matching, Two-Sided Incomplete Information, and Participation Costs: Existence and Convergence to Perfect Competition," Econometrica, Econometric Society, vol. 75(1), pages 155-200, 01. [Downloadable!] (restricted)
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  9. Wolinsky, Asher, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Blackwell Publishing, vol. 55(1), pages 71-84, January. [Downloadable!] (restricted)
  10. Alp E. Atakan, 2006. "Competitive Equilibria in Decentralized Matching with Incomplete Information," Discussion Papers 1437, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  11. 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. [Downloadable!] (restricted)
  12. Richard Rogerson & Robert Shimer & Randall Wright, 2005. "Search-Theoretic Models of the Labor Market: A Survey," Journal of Economic Literature, American Economic Association, vol. 43(4), pages 959-988, December. [Downloadable!] (restricted)
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  13. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-50, September. [Downloadable!] (restricted)
  14. Tymon Tatur, 2005. "On the Trade off Between Deficit and Inefficiency and the Double Auction with a Fixed Transaction Fee," Econometrica, Econometric Society, vol. 73(2), pages 517-570, 03. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Edward W. Piotrowski & Jan Sladkowski & Anna Szczypinska, 2007. "Reinforcement learning in market games," Quantitative Finance Papers 0710.0114, arXiv.org. [Downloadable!]
  2. Edward W. Piotrowski & Jan Sladkowski & Anna Szczypinska, . "Reinforcement Learning in Market Games," Departmental Working Papers 30, University of Bialtystok, Department of Theoretical Physics. [Downloadable!]
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