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| Benjamin Tello |
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| ''Stability and Contractual Efficiency in Matching with Contracts and Lexicographic Preferences'' |
| ( 2022, Vol. 42 No.1 ) |
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| 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. |
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| Keywords: matching, stability, contractual efficiency, lexicographic preferences |
JEL: C7 - Game Theory and Bargaining Theory
D6 - Welfare Economics: General |
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| Manuscript Received : Nov 23 2021 | | Manuscript Accepted : Feb 20 2022 |
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