Hedonic clustering games

Moran Feldman, Liane Lewin-Eytan, Joseph Naor

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - May 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 ACM.


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


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