Ordinal and cardinal solution concepts for two-sided matching . Echenique, F. & Galichon, A. Games and Economic Behavior , 101(1):63-77 , 2017.
Ordinal and cardinal solution concepts for two-sided matching  [link]Paper  doi  abstract   bibtex   
Abstract We characterize solutions for two-sided matching, both in the transferable- and in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade stable matching to study the role of transfers in matching. A no-trade stable matching is one in which the availability of transfers does not affect the outcome.
@article{EcheniqueGalichon2015,
title = "Ordinal and cardinal solution concepts for two-sided matching ",
journal = "Games and Economic Behavior ",
volume = "101",
number = "1",
pages = " 63-77 ",
year = "2017",
note = "",
issn = "0899-8256",
doi = "http://dx.doi.org/10.1016/j.geb.2015.10.002",
url = "http://www.sciencedirect.com/science/article/pii/S0899825615001323",
author = "Federico Echenique and Alfred Galichon",
keywords = "Market design",
keywords = "Matching theory",
keywords = "National resident matching program ",
abstract = "Abstract We characterize solutions for two-sided matching, both in the transferable- and in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade stable matching to study the role of transfers in matching. A no-trade stable matching is one in which the availability of transfers does not affect the outcome. "
}

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