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Sorting and Decentralized Price Competition

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Author Info
Jan Eeckhout () (Department of Economics, University of Pennsylvania)
Philipp Kircher () (Department of Economics, University of Pennsylvania)
Abstract

We investigate under which conditions price competition in a market with matching frictions leads to sorting of buyers and sellers. Positive assortative matching obtains only if there is a high enough degree of complementarity between buyer and seller types. The relevant condition is root-supermodularity; i.e., the square root of the match value function is supermodular. It is a necessary and sufficient condition for positive assortative matching under any distribution of buyer and seller types, and does not depend on the details of the underlying matching function that describes the search process. The condition is weaker than log-supermodularity, a condition required for positive assortative matching in markets with random search. This highlights the role competition plays in matching heterogeneous agents. Negative assortative matching obtains whenever the match value function is weakly submodular.

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Publisher Info
Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 08-020.

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Length: 47 pages
Date of creation: 01 May 2008
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Handle: RePEc:pen:papers:08-020

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Related research
Keywords: Competitive Search Equilibrium. Directed Search. Two-Sided Matching. Decentralized Price Competition. Root-Supermodularity.

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Find related papers by JEL classification:
J64 - Labor and Demographic Economics - - Mobility, Unemployment, and Vacancies - - - Unemployment: Models, Duration, Incidence, and Job Search
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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  1. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October. [Downloadable!] (restricted)
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    Other versions:
  3. 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)
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  5. Lones Smith, 2006. "The Marriage Model with Search Frictions," Journal of Political Economy, University of Chicago Press, vol. 114(6), pages 1124-1146, December. [Downloadable!] (restricted)
  6. Peters, Michael, 2000. "Limits of Exact Equilibria for Capacity Constrained Sellers with Costly Search," Journal of Economic Theory, Elsevier, vol. 95(2), pages 139-168, December. [Downloadable!] (restricted)
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  7. Peters, Michael, 1997. "A Competitive Distribution of Auctions," Review of Economic Studies, Blackwell Publishing, vol. 64(1), pages 97-123, January. [Downloadable!] (restricted)
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  8. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July. [Downloadable!] (restricted)
  9. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October. [Downloadable!] (restricted)
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  10. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug.. [Downloadable!] (restricted)
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  11. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
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  12. Michael Peters, 1995. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The case of Complete Contracts," Working Papers peters-95-01, University of Toronto, Department of Economics. [Downloadable!]
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  13. Peters, Michael, 2005. "Unobservable Heterogeneity in Directed Search," Micro Theory Working Papers peters-05-06-13-01-50-30, Microeconomics.ca Website, revised 22 May 2008. [Downloadable!]
  14. Alain Delacroix & Shouyong Shi, 2003. "Directed Search On the Job and the Wage Ladder," Working Papers shouyong-03-04, University of Toronto, Department of Economics. [Downloadable!]
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  15. Manolis Galenianos & Philipp A. Kircher, 2005. "Directed Search with Multiple Job Applications," Bonn Econ Discussion Papers bgse20_2005, University of Bonn, Germany. [Downloadable!]
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  16. Hoppe, Heidrun C. & Moldovanu, Benny & Sela, Aner, 2006. "The Theory of Assortative Matching Based on Costly Signals," CEPR Discussion Papers 5543, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  17. Burdett, Ken & Coles, Melvyn G, 1997. "Marriage and Class," The Quarterly Journal of Economics, MIT Press, vol. 112(1), pages 141-68, February.
  18. Shi, Shouyong, 2002. "A Directed Search Model of Inequality with Heterogeneous Skills and Skill-Based Technology," Review of Economic Studies, Blackwell Publishing, vol. 69(2), pages 467-91, April.
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  20. Acemoglu, Daron & Shimer, Robert, 1999. "Holdups and Efficiency with Search Frictions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 827-49, November.
    Other versions:
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