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Profit-Maximizing Matchmaker


  • Hideo Konishi

    () (Boston College)

  • Chiu Yu Ko

    (Boston College)


This paper considers a resource allocation mechanism that utilizes a profit-maximizing auctioneer/matchmaker in the Kelso-Crawford (1982) (many-to-one) assignment problem. We consider general and simple (individualized price) message spaces for firms' reports following Milgrom (2010). We show that in the simple message space, (i) the matchmaker's profit is always zero and an acceptable assignment is achieved in every Nash equilibrium, and (ii) the sets of stable assignments and strong Nash equilibria are equivalent. By contrast, in the general message space, the matchmaker may make a positive profit even in a strong Nash equilibrium. This shows that restricting message space not only reduces the information requirement but also improves resource allocation.

Suggested Citation

  • Hideo Konishi & Chiu Yu Ko, 2009. "Profit-Maximizing Matchmaker," Boston College Working Papers in Economics 721, Boston College Department of Economics, revised 23 Apr 2012.
  • Handle: RePEc:boc:bocoec:721

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    References listed on IDEAS

    1. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    2. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, March.
    3. Shin, Sungwhee & Suh, Sang-Chul, 1996. "A mechanism implementing the stable rule in marriage problems," Economics Letters, Elsevier, vol. 51(2), pages 185-189, May.
    4. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    5. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, March.
    6. Sonmez, Tayfun, 1997. "Games of Manipulation in Marriage Problems," Games and Economic Behavior, Elsevier, vol. 20(2), pages 169-176, August.
    7. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    8. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    9. Laussel, Didier & Le Breton, Michel, 2001. "Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency," Journal of Economic Theory, Elsevier, vol. 100(1), pages 93-128, September.
    10. Milgrom, Paul, 2010. "Simplified mechanisms with an application to sponsored-search auctions," Games and Economic Behavior, Elsevier, vol. 70(1), pages 62-70, September.
    11. B. Douglas Bernheim & Michael D. Whinston, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, Oxford University Press, vol. 101(1), pages 1-31.
    12. Takashi Hayashi & Toyotaka Sakai, 2009. "Nash implementation of competitive equilibria in the job-matching market," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 453-467, November.
    13. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1999. "On Coalition-Proof Nash Equilibria in Common Agency Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 122-139, March.
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    More about this item


    two-sided matching problem; stable assignment; strong Nash equilibrium; coalition-proof Nash equilibrium; no-rent property; implementation theory;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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