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

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  • Shneyerov, Art
  • Wong, Adam Chi Leung

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.

Suggested Citation

  • 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.
  • Handle: RePEc:ubc:pmicro:shneyerov-07-05-01-03-43-25
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    File URL: http://microeconomics.ca/artyom_shneyerov/srate.pdf
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    References listed on IDEAS

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    1. 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, January.
    2. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "Bilateral matching and bargaining with private information," Games and Economic Behavior, Elsevier, vol. 68(2), pages 748-762, March.
    3. Serrano, Roberto, 2002. "Decentralized information and the Walrasian outcome: a pairwise meetings market with private values," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 65-89, September.
    4. 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.
    5. 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.
    6. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    7. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    8. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    9. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
    10. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-818, July.
    11. Asher Wolinsky, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 71-84.
    12. 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, March.
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    Cited by:

    1. Edward W. Piotrowski & Jan Sladkowski & Anna Szczypinska, "undated". "Reinforcement Learning in Market Games," Departmental Working Papers 30, University of Bialtystok, Department of Theoretical Physics.
    2. 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.

    More about this item

    Keywords

    Matching and Bargaining; Search; Double Auctions; Foundations for Perfect Competition; Rate of Convergence;

    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; Information and Knowledge; Communication; Belief; Unawareness

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