The Complexity of Rationalizing Matchings

  • Shankar Kalyanaraman
  • Christopher Umans
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Shankar Kalyanaraman
    • 1
  • Christopher Umans
    • 1
  1. 1.Computer Science DepartmentCalifornia Institute of TechnologyPasadenaUSA

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