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Equivalence of Canonical Matching Models

Author

Listed:
  • John Kennes

    () (Department of Economics and Business Economics, Aarhus University, Denmark)

  • Daniel le Maire

    (University of Copenhagen)

  • Sebastian Roelsgaard

    (Department of Economics and Business Economics, Aarhus University, Denmark)

Abstract

This paper offers expected revenue and pricing equivalence results for canonical models of pricing and matching. The equivalence of these models is centered on the assumption that there are large numbers of buyers and sellers and the assignment of buyers within a submarket of sellers is random. Therefore, the distribution of buyers to sellers is approximated by the Poisson distribution. The list of canonical matching models includes the models developed by Burdett and Judd (1983), Shimer (2005), and McAfee (1993). In the Burdett and Judd (1983) model, buyers post prices and the equilibrium features price dispersion because identical buyers play mixed strategies. In the Shimer (2005) model, sellers post a vector of prices corresponding to different buyer types. In equilibrium, all identical buyers pay the same price. In the McAfee (1993) model, equilibrium pricing is determined by simple second price auctions. McAfee’s model also features price dispersion, because the number of bidders at each auction is stocastic.

Suggested Citation

  • John Kennes & Daniel le Maire & Sebastian Roelsgaard, 2018. "Equivalence of Canonical Matching Models," Economics Working Papers 2018-08, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2018-08
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    File URL: ftp://ftp.econ.au.dk/afn/wp/18/wp18_08.pdf
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    References listed on IDEAS

    as
    1. Julien, Benoit & Kennes, John & King, Ian, 2006. "The Mortensen rule and efficient coordination unemployment," Economics Letters, Elsevier, vol. 90(2), pages 149-155, February.
    2. Kultti, Klaus, 1999. "Equivalence of Auctions and Posted Prices," Games and Economic Behavior, Elsevier, vol. 27(1), pages 106-113, April.
    3. John Kennes & Daniel le Maire, 2013. "Competing Auctions of Skills," CAM Working Papers 2014_01, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    4. Gabriele Camera & Cemil Selcuk, 2009. "Price Dispersion with Directed Search," Journal of the European Economic Association, MIT Press, vol. 7(6), pages 1193-1224, December.
    5. Alex Xi He & John Kennes & Daniel le Maire, 2018. "Complementarity and Advantage in the Competing Auctions of Skills," Economics Working Papers 2018-10, Department of Economics and Business Economics, Aarhus University.
    6. Diamond, Peter A., 1971. "A model of price adjustment," Journal of Economic Theory, Elsevier, vol. 3(2), pages 156-168, June.
    7. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    8. Hall, Robert E., 1979. "A theory of the natural unemployment rate and the duration of employment," Journal of Monetary Economics, Elsevier, vol. 5(2), pages 153-169, April.
    9. Shouyong Shi & Alain Delacroix, 2018. "Should Buyers or Sellers Organize Trade in a Frictional Market?," The Quarterly Journal of Economics, Oxford University Press, vol. 133(4), pages 2171-2214.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Directed search; price dispersion; competing auctions; Poisson distribution;

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

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