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Price Setting in a Decentralized Market and the Competitive Outcome

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  • Stephan Lauermann

    (University of Bonn)

Abstract

This paper studies a decentralized, dynamic matching and bargaining market: buyers and sellers are matched into pairs. Traders exit the market at a constant rate, inducing search costs (frictions). All price offers are made by sellers. Despite the fact that sellers have all the bargaining power we show that they set competitive prices in the limit when frictions become small. Previous literature has restricted the sellers' bargaining power. We dispense with this restriction and show that the convergence result does not depend on the distribution of bargaining power. Our model allows us to isolate basic market clearing forces that ensure the competitive outcome in the frictionless limit. For the particular case of homogeneous sellers we characterize the equilibrium price by the familiar Lerner formula. We use this formula to provide comparative static results of the decentralized trading outcome with respect to the level of the search frictions.

Suggested Citation

  • 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.
    • Handle: RePEc:mpg:wpaper:2008_6
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    File URL: http://www.coll.mpg.de/pdf_dat/2008_06online.pdf
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    References listed on IDEAS

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    1. Igal Hendel & Aviv Nevo, 2006. "Measuring the Implications of Sales and Consumer Inventory Behavior," Econometrica, Econometric Society, vol. 74(6), pages 1637-1673, November.
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    3. 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.
    4. 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.
    5. Gale,Douglas, 2000. "Strategic Foundations of General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521644105, January.
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    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
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    18. Igal Hendel & Aviv Nevo, 2006. "Sales and Consumer Inventory," RAND Journal of Economics, The RAND Corporation, vol. 37(3), pages 543-561, Autumn.
    19. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    20. Larry Samuelson, 1992. "Disagreement in Markets with Matching and Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 177-185.
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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, vol. 68(2), pages 748-762, March.
    2. 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.
    3. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    4. Lauermann, Stephan, 2012. "Asymmetric information in bilateral trade and in markets: An inversion result," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1969-1997.

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    More about this item

    Keywords

    Dynamic Matching and Bargaining Games; Decentralized Markets; Non-cooperative Foundations of Competitive Equilibrium; Search Frictions; Rationing;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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