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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.

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Bibliographic Info

Paper provided by Vancouver School of Economics in its series Microeconomics.ca 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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Web page: http://www.economics.ubc.ca/

Related research

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

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References

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  1. 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.
  2. Lauermann, Stephan, 2011. "Dynamic matching and bargaining games: A general approach," MPRA Paper 31717, University Library of Munich, Germany.
  3. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-50, September.
  4. Shneyerov, Art & Wong, Adam Chi Leung, 2007. "Bilateral Matching and Bargaining with Private Information," Microeconomics.ca working papers shneyerov-07-05-01-03-38-, Vancouver School of Economics, revised 01 May 2007.
  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. 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.
  7. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
  8. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July.
  9. Wolinsky, Asher, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Wiley Blackwell, vol. 55(1), pages 71-84, January.
  10. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  11. Gianni De Fraja & Jozsef Sakovics, 2004. "Walras Retrouve: Decentralized Trading Mechanisms and the Competitive Price," ESE Discussion Papers 36, Edinburgh School of Economics, University of Edinburgh.
  12. Satterthwaite, Mark & Shneyerov, Art, 2004. "Dynamic Matching,Two-sided Incomplete Information, and Participation Costs: Existence and Convergence to Perfect Competition," Microeconomics.ca working papers shneyerov-04-12-17-02-54-, Vancouver School of Economics, revised 17 Dec 2004.
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Cited by:
  1. Edward W. Piotrowski & Jan Sladkowski & Anna Szczypinska, . "Reinforcement Learning in Market Games," Departmental Working Papers 30, University of Bialtystok, Department of Theoretical Physics.

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