IDEAS home Printed from https://ideas.repec.org/p/pen/papers/08-020.html
   My bibliography  Save this paper

Sorting and Decentralized Price Competition

Author

Listed:
  • 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.

Suggested Citation

  • Jan Eeckhout & Philipp Kircher, 2008. "Sorting and Decentralized Price Competition," PIER Working Paper Archive 08-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:08-020
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/working-papers/08-020.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293, December.
    2. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    3. 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.
    4. Galenianos, Manolis & Kircher, Philipp, 2009. "Directed search with multiple job applications," Journal of Economic Theory, Elsevier, vol. 144(2), pages 445-471, March.
    5. Larry Samuelson & Andrew Postlewaite & George Mailath, 2007. "Pricing in Matching Markets," 2007 Meeting Papers 531, Society for Economic Dynamics.
    6. Philipp Kircher & Jan Eeckhout, 2008. "Prices as Optimal Competitive Sales Mechanisms," 2008 Meeting Papers 504, Society for Economic Dynamics.
    7. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October.
    8. 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.
    9. Shouyong Shi, 1998. "Frictional Assignment," Working Paper 988, Economics Department, Queen's University.
    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. Michael Peters, 1997. "A Competitive Distribution of Auctions," Review of Economic Studies, Oxford University Press, vol. 64(1), pages 97-123.
    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.
    13. Guillaume Rocheteau & Randall Wright, 2005. "Money in Search Equilibrium, in Competitive Equilibrium, and in Competitive Search Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 175-202, January.
    14. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2009. "The Theory of Assortative Matching Based on Costly Signals," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 253-281.
    15. Lones Smith, 2006. "The Marriage Model with Search Frictions," Journal of Political Economy, University of Chicago Press, vol. 114(6), pages 1124-1146, December.
    16. Philipp Kircher, 2009. "Efficiency of Simultaneous Search," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 861-913, October.
    17. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    18. Guido Menzio, 2007. "A Theory of Partially Directed Search," Journal of Political Economy, University of Chicago Press, vol. 115(5), pages 748-769, October.
    19. Ken Burdett & Melvyn G. Coles, 1997. "Marriage and Class," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 141-168.
    20. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    21. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    22. Shouyong Shi, 2002. "A Directed Search Model of Inequality with Heterogeneous Skills and Skill-Biased Technology," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 467-491.
    23. 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 827-849, November.
    24. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
    25. 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.
    26. Michael Peters, 1997. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The Case of Complete Contracts," Review of Economic Studies, Oxford University Press, vol. 64(2), pages 241-264.
    27. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
    28. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    29. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    30. Alain Delacroix & Shouyong Shi, 2006. "Directed Search On The Job And The Wage Ladder," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 651-699, May.
    31. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-818, July.
    32. Kiyotaki, Nobuhiro & Wright, Randall, 1993. "A Search-Theoretic Approach to Monetary Economics," American Economic Review, American Economic Association, vol. 83(1), pages 63-77, March.
    33. Robert Shimer, 2005. "The Assignment of Workers to Jobs in an Economy with Coordination Frictions," Journal of Political Economy, University of Chicago Press, vol. 113(5), pages 996-1025, October.
    34. Gerard R. Butters, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 465-491.
    35. Arthur J. Hosios, 1990. "On The Efficiency of Matching and Related Models of Search and Unemployment," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 279-298.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philipp Kircher, 2009. "Efficiency of Simultaneous Search," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 861-913, October.
    2. Eeckhout, Jan & Kircher, Philipp, 2010. "Sorting versus screening: Search frictions and competing mechanisms," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1354-1385, July.
    3. Richard Rogerson & Robert Shimer & Randall Wright, 2004. "Search-Theoretic Models of the Labor Market-A Survey," NBER Working Papers 10655, National Bureau of Economic Research, Inc.
    4. Cai, Xiaoming & Gautier, Pieter A. & Wolthoff, Ronald P., 2017. "Search frictions, competing mechanisms and optimal market segmentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 453-473.
    5. Manolis Galenianos & Philipp Kircher, 2012. "On The Game‐Theoretic Foundations Of Competitive Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 1-21, February.
    6. Galenianos, Manolis & Kircher, Philipp, 2009. "Directed search with multiple job applications," Journal of Economic Theory, Elsevier, vol. 144(2), pages 445-471, March.
    7. Mangin, Sephorah, 2017. "A theory of production, matching, and distribution," Journal of Economic Theory, Elsevier, vol. 172(C), pages 376-409.
    8. Makoto Watanabe, 2018. "Middle Men: The Visible Market-Makers," The Japanese Economic Review, Springer, vol. 69(2), pages 156-170, June.
    9. Paulina Restrepo-Echavarria & Antonella Tutino & Anton Cheremukhin, 2013. "A Theory of Targeted Search," 2013 Meeting Papers 664, Society for Economic Dynamics.
    10. Guerrieri, Veronica & Julien, Benoit & Kircher, Philipp & Wright, Randall, 2017. "Directed Search: A Guided Tour," CEPR Discussion Papers 12315, C.E.P.R. Discussion Papers.
    11. Jerez, Belén, 2014. "Competitive equilibrium with search frictions: A general equilibrium approach," Journal of Economic Theory, Elsevier, vol. 153(C), pages 252-286.
    12. Jerez, Belén, 2017. "Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments," Journal of Economic Theory, Elsevier, vol. 172(C), pages 202-219.
    13. Shouyong Shi, 2005. "Frictional Assignment, Part II: Infinite Horizon and Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(1), pages 106-137, January.
    14. Manolis Galenianos & Philipp Kircher, 2007. "Heterogeneous Firms in a Finite Directed Search Economy," PIER Working Paper Archive 07-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    15. Richard Dutu & Benoit Julien & Ian King, 2009. "Liquidity Constrained Competing Auctions," Department of Economics - Working Papers Series 1068, The University of Melbourne.
    16. Hector Chade & Jan Eeckhout & Lones Smith, 2017. "Sorting through Search and Matching Models in Economics," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 493-544, June.
    17. Lester, Benjamin & Visschers, Ludo & Wolthoff, Ronald, 2015. "Meeting technologies and optimal trading mechanisms in competitive search markets," Journal of Economic Theory, Elsevier, vol. 155(C), pages 1-15.
    18. Cai, Xiaoming & Gautier, Pieter A. & Wolthoff, Ronald P., 2021. "Search, Screening and Sorting," IZA Discussion Papers 14501, Institute of Labor Economics (IZA).
    19. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    20. Albrecht, James & Cai, Xiaoming & Gautier, Pieter & Vroman, Susan, 2020. "Multiple applications, competing mechanisms, and market power," Journal of Economic Theory, Elsevier, vol. 190(C).

    More about this item

    Keywords

    Competitive Search Equilibrium. Directed Search. Two-Sided Matching. Decentralized Price Competition. Root-Supermodularity.;

    JEL classification:

    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - 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; Information and Knowledge; Communication; Belief; Unawareness

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pen:papers:08-020. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/deupaus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.