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Competitive Equilibria in Decentralized Matching with Incomplete Information

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  • Alp E. Atakan

Abstract

This paper shows that all perfect Bayesian equilibria of a decentralized dynamic matching market with two-sided incomplete information of independent private values variety converge to competitive equilibria. Each buyer wants to purchase a bundle of heterogeneous, indivisible goods and each seller owns one unit of a heterogeneous indivisible good (as in Kelso and Crawford (1982) or Gul and Stacchetti (1999)). Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through bilateral bargaining between buyers and sellers. The paper considers a market in steady state. It is shown that as frictions, i.e., discounting and fixed costs of search become small, all equilibria of the market game converge to perfectly competitive equilibria.

Suggested Citation

  • 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.
  • Handle: RePEc:nwu:cmsems:1437
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    References listed on IDEAS

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    1. Myerson, Roger B, 1983. "Mechanism Design by an Informed Principal," Econometrica, Econometric Society, vol. 51(6), pages 1767-1797, November.
    2. Serrano, Roberto, 2002. "Decentralized information and the Walrasian outcome: a pairwise meetings market with private values," Journal of Mathematical Economics, Elsevier, pages 65-89.
    3. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, pages 663-689.
    4. Maskin, Eric & Tirole, Jean, 1990. "The Principal-Agent Relationship with an Informed Principal: The Case of Private Values," Econometrica, Econometric Society, vol. 58(2), pages 379-409, March.
    5. John G. Riley & Richard Zeckhauser, 1980. "Optimal Selling Strategies:," UCLA Economics Working Papers 180, UCLA Department of Economics.
    6. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, pages 20-54.
    7. Yilankaya, Okan, 1999. "A Note on the Seller's Optimal Mechanism in Bilateral Trade with Two-Sided Incomplete Information," Journal of Economic Theory, Elsevier, vol. 87(1), pages 267-271, July.
    8. 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.
    9. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 267-289.
    10. Moreno, Diego & Wooders, John, 2002. "Prices, Delay, and the Dynamics of Trade," Journal of Economic Theory, Elsevier, vol. 104(2), pages 304-339, June.
    11. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    12. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    13. Wolinsky, Asher, 1990. "Information Revelation in a Market with Pairwise Meetings," Econometrica, Econometric Society, pages 1-23.
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    Citations

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    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. Simon Loertscher & Andras Niedermayer, 2008. "Fee Setting Intermediaries: On Real Estate Agents, Stock Brokers, and Auction Houses," Discussion Papers 1472, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. 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.
    4. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "The rate of convergence to perfect competition of matching and bargaining mechanisms," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1164-1187, May.
    5. Stephan Lauermann, 2008. "When Less Information is Good for Efficiency: Private Information in Bilateral Trade and in Markets," 2008 Meeting Papers 419, Society for Economic Dynamics.
    6. Niedermayer, Andras & Shneyerov, Artyom, 2013. "For-Profit Search Platforms," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 436, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    7. 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.
    8. Werner Güth & René Levínský & Kerstin Pull & Ori Weisel, 2016. "Tournaments and piece rates revisited: a theoretical and experimental study of output-dependent prize tournaments," Review of Economic Design, Springer;Society for Economic Design, pages 69-88.
    9. Stephan Lauermann, 2008. "Price Setting in a Decentralized Market and the Competitive Outcome," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2008_06, Max Planck Institute for Research on Collective Goods.
    10. 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.

    More about this item

    Keywords

    Bargaining; Search; Matching;

    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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