Article

The Complexity of Rationalizing Matchings

Authors:

Shankar Kalyanaraman,

Christopher UmansAuthors Info & Claims

ISAAC '08: Proceedings of the 19th International Symposium on Algorithms and Computation

Pages 171 - 182

https://doi.org/10.1007/978-3-540-92182-0_18

Published: 15 December 2008 Publication History

Abstract

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.

Cited By

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Wu JShen WFang FXu HKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Inverse game theory for stackelberg gamesProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602602(32186-32198)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602602
Kuleshov VSchrijvers O(2015)Inverse Game Theory: Learning Utilities in Succinct GamesWeb and Internet Economics10.1007/978-3-662-48995-6_30(413-427)Online publication date: 9-Dec-2015
https://dl.acm.org/doi/10.1007/978-3-662-48995-6_30
Smeulders BSpieksma FCherchye LDe Rock B(2014)Goodness-of-Fit Measures for Revealed Preference TestsACM Transactions on Economics and Computation10.1145/25607932:1(1-16)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1145/2560793

The Complexity of Rationalizing Matchings
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis

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Published In

ISAAC '08: Proceedings of the 19th International Symposium on Algorithms and Computation

December 2008

942 pages

ISBN:9783540921813

Editors:
Seok-Hee Hong
School of Information Technologies, University of Sydney, Australia
,
Hiroshi Nagamochi
Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501
,
Takuro Fukunaga
Graduate School of Informatics, Kyoto University, Japan

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 December 2008

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Wu JShen WFang FXu HKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Inverse game theory for stackelberg gamesProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602602(32186-32198)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602602
Kuleshov VSchrijvers O(2015)Inverse Game Theory: Learning Utilities in Succinct GamesWeb and Internet Economics10.1007/978-3-662-48995-6_30(413-427)Online publication date: 9-Dec-2015
https://dl.acm.org/doi/10.1007/978-3-662-48995-6_30
Smeulders BSpieksma FCherchye LDe Rock B(2014)Goodness-of-Fit Measures for Revealed Preference TestsACM Transactions on Economics and Computation10.1145/25607932:1(1-16)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1145/2560793

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