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Assortative Matching, Reputation, and the Beatles Break-Up

Author

Listed:
  • Lones Smith

    (University of Michigan)

  • Axel Anderson

    (University of Michigan)

Abstract

Consider Becker's (1973) classic static matching model, with output a stochastic function of unobserved types. Assume symmetric incomplete information about types, and thus commonly observed Bayesian posteriors. Matching is then assortative in these `reputations' if expected output is supermodular in types. We instead consider a standard dynamic version of this world, and discover a robust failure of Becker's global result. We show that as the production outcomes grow, assortative matching is neither efficient nor an equilibrium for high enough discount factors. Specifically, assortative matching fails around the highest reputation agents for `low-skill concealing' technologies. Our theory implies the dynamic result that high-skill matches (like the Beatles) eventually break~up. Our results owe especially to two findings: (a) value convexity due to learning undermines match supermodularity; and (b) for a fixed policy in optimal learning, the second derivative of the value function explodes geometrically at extremes.

Suggested Citation

  • Lones Smith & Axel Anderson, 2002. "Assortative Matching, Reputation, and the Beatles Break-Up," Game Theory and Information 0201002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0201002
    Note: Type of Document - ; prepared on PC; to print on HP; pages: 23; figures: included
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0201/0201002.pdf
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    References listed on IDEAS

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    1. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    2. Kremer, M & Maskin, E, 1996. "Wage Inequality and Segregation by Skill," Working papers 96-23, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 103-127, January.
    4. Lones Smith, 2006. "The Marriage Model with Search Frictions," Journal of Political Economy, University of Chicago Press, vol. 114(6), pages 1124-1146, December.
    5. Wolinsky, Asher, 1990. "Information Revelation in a Market with Pairwise Meetings," Econometrica, Econometric Society, vol. 58(1), pages 1-23, January.
    6. Ken Burdett & Melvyn G. Coles, 1997. "Marriage and Class," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 141-168.
    7. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    8. 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..
    9. Michael Kremer & Eric Maskin, 1996. "Wage Inequality and Segregation," Harvard Institute of Economic Research Working Papers 1777, Harvard - Institute of Economic Research.
    10. Mortensen, Dale T, 1982. "Property Rights and Efficiency in Mating, Racing, and Related Games," American Economic Review, American Economic Association, vol. 72(5), pages 968-979, December.
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    Cited by:

    1. Thomas Gall & David Reinstein, 2020. "Losing face," Oxford Economic Papers, Oxford University Press, vol. 72(1), pages 164-190.
    2. Chade, Hector, 2006. "Matching with noise and the acceptance curse," Journal of Economic Theory, Elsevier, vol. 129(1), pages 81-113, July.
    3. Heski Bar-Isaac, 2004. "Something to Prove: Reputation in teams and hiring to introduce uncertainty," Working Papers 04-07, New York University, Leonard N. Stern School of Business, Department of Economics.
    4. Aloysius Siow & Eugene Choo, 2007. "Lifecycle marriage matching: Theory and Evidence," 2007 Meeting Papers 550, Society for Economic Dynamics.

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    More about this item

    Keywords

    supermodularity; convexity;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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