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Profit-Maximizing Matchmaker

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Author Info
Hideo Konishi () (Boston College)
Chiu Yu Ko (Boston College)

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Abstract

This paper considers a matchmaker game in the Shapley-Shubik (1971) (one-to-one) assignment problem. Each firm proposes how much it is willing to pay each worker if they are matched. Each worker also proposes which salary she is willing to accept from each firm if they are matched. The matchmaker chooses a matching to maximize profit (the sum of the difference between the offering and asking salaries from each matched firm-worker). First, we show that Nash equilibrium may generate inefficient outcomes, but the matchmaker's profit is always zero in every Nash equilibrium. Second, we show that the sets of stable assignments and strong Nash equilibria are equivalent. These results extend to the Kelso-Crawford (1982) many-to-one assignment problem. Interestingly, in the one-to-one matching case, our results are closely related to the common agency game by Bernheim and Whinston (1986), while in the many-to-one assignment problem, such relationships break down completely.

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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 721.

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Date of creation: 28 Oct 2009
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Handle: RePEc:boc:bocoec:721

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

Find related papers by 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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This page was last updated on 2009-11-24.

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