Fractional hedonic games

Abstract

An important issue in multi-agent systems is the exploitation of synergies via coalition formation. We initiate the formal study of fractional hedonic games. In fractional hedonic games, the utility of a player in a coalition structure is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which there are several types of agents and each agent desires to be in a coalition in which the fraction of agents of his own type is minimal. Fractional hedonic games not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of fractional hedonic games is non-empty and provide algorithms for computing a core stable outcome.