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The Complexity of Rationalizing Matchings

Kalyanaraman, Shankar and Umans, Christopher (2008) The Complexity of Rationalizing Matchings. Electronic Colloquium on Computational Complexity . Art. No. 21. ISSN 1433-8092.

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Given a set of observed economic choices, can one infer preferences and/or utility functions for the players that are consistent with the data? Questions of this type are called rationalization or revealed preference problems in the economic literature, and are the subject of a rich body of work. From the computer science perspective, it is natural to study the complexity of rationalization in various scenarios. We consider a class of rationalization problems in which the economic data is expressed by a collection of matchings, and the question is whether there exist preference orderings for the nodes under which all the matchings are stable. We show that the rationalization problem for one-one matchings is NP-complete. We propose two natural notions of approximation, and show that the problem is hard to approximate to within a constant factor, under both. On the positive side, we describe a simple algorithm that achieves a 3/4 approximation ratio for one of these approximation notions. We also prove similar results for a version of many-one matching.

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Additional Information:© 2008 Computational Complexity Foundation (CCF). Supported by NSF CCF-0346991, BSF 2004329 and a Graduate Research Fellowship from the Social and Information Sciences Laboratory (SISL) at Caltech. Supported by NSF CCF-0346991, BSF 2004329, a Sloan Research Fellowship, and an Okawa Foundation research grant. We are indebted to Federico Echenique for numerous invaluable discussions and for getting us started on this work.
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Binational Science Foundation (USA-Israel)2004329
Caltech Social and Information Sciences LaboratoryUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Okawa FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20191127-084809601
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100089
Deposited By: Tony Diaz
Deposited On:27 Nov 2019 17:00
Last Modified:27 Nov 2019 17:00

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