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Benjamin Tello
''Stability and Contractual Efficiency in Matching with Contracts and Lexicographic Preferences''
( 2022, Vol. 0 No.0 )
We introduce an efficiency concept in matching markets with contracts called contractual efficiency. Contractual efficiency requires that each student is assigned to a school under her most preferred contractual term. We show that while in general it is not possible to have stable and contractually efficient matchings; if the preferences of each school are lexicographic, then there is a contractually efficient and stable matching. Moreover, we provided an algorithm, the Best-Term Deferred Acceptance (Best-Term DA) algorithm, that produces a contractually efficient and stable matching whenever schools' preferences are lexicographic. Finally, we turn to the question of whether a contractually efficient and stable matching can be implemented in dominant strategies. We show that in a two-stage matching market whereby contractual terms can be interpreted as pre-matching investments -each student first chooses her investment and then students and schools match according to the School-Optimal Stable Matching-, it is a dominant strategy for each student to choose the investment associated with the outcome of the Best-Term DA algorithm and the outcome of the two-stage market is precisely the outcome of the Best-Term DA algorithm.
Keywords: matching, stability, contractual efficiency, lexicographic preferences
JEL: C7 - Game Theory and Bargaining Theory
D6 - Welfare Economics: General
Manuscript Received : Nov 23 2021 Manuscript Accepted : Feb 20 2022

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