Hedonic clustering games

Moran Feldman, Liane Lewin-Eytan, Joseph Naor

Research output: Contribution to journalArticlepeer-review

Abstract

Clustering, the partitioning of objects with respect to a similarity measure, has been extensively studied as a global optimization problem. We investigate clustering from a game-theoretic approach, and consider the class of hedonic clustering games. Here, a self-organized clustering is obtained via decisions made by independent players, corresponding to the elements clustered. Being a hedonic setting, the utility of each player is determined by the identity of the othermembers of her cluster. This class of games seems to be quite robust, as it fits with rather different, yet commonly used, clustering criteria. Specifically, we investigate hedonic clustering games in two different models: fixed clustering, which subdivides into k-median and k-center, and correlation clustering. We provide a thorough analysis of these games, characterizing Nash equilibria, and proving upper and lower bounds on the price of anarchy and price of stability. For fixed clustering we focus on the existence of a Nash equilibrium, as it is a rather nontrivial issue in this setting. We study it both for general metrics and special cases, such as line and tree metrics. In the correlation clustering model, we study both minimization and maximization variants, and provide almost tight bounds on both the price of anarchy and price of stability.

Original languageEnglish
Article numbera4
JournalACM Transactions on Parallel Computing
Volume2
Issue number1
DOIs
StatePublished - May 2015
Externally publishedYes

Bibliographical note

Funding Information:
Work supported in part by the Technion-Microsoft Electronic Commerce Research Center and by ISF grant 954/11. A preliminary version of this work appeared in Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA12), pages 267-276.

Funding Information:
Work supported in part by the Technion-Microsoft Electronic Commerce Research Center and by ISF grant 954/11. A preliminary version of this work appeared in Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA12), pages 267–276. Authors’ addresses: M. Feldman (current address), EPFL-IC-THL2, Station 14, 1015 Lausanne, Switzerland; email: moran.feldman@epfl.ch; L. Lewin-Eytan, Yahoo Labs, Haifa, Israel; email: liane@yahoo-inc.com; J. (Seffi) Naor, CS Dept., Technion, Haifa, Israel; email: naor@cs.technion.ac.il. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. ©c 2015 ACM 2329-4949/2015/05-ART4 $15.00 DOI: http://dx.doi.org/10.1145/2742345

Publisher Copyright:
© 2015 ACM.

Keywords

  • Clustering games
  • Hedonic games
  • Price of anarchy
  • Price of stability

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Hardware and Architecture
  • Computer Science Applications
  • Computational Theory and Mathematics

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