Coalition formation is a fundamental problem in the orga-nization of many multi-agent systems. In large populations, the formation of coalitions is often restricted by structural visibility and locality constraints under which agents can re-organize. We capture and study this aspect using a novel network-based model for dynamic locality within the pop-ular framework of hedonic coalition formation games. We analyze the effects of network-based visibility and structure on the convergence of coalition formation processes to sta-ble states. Our main result is a tight characterization of the structures based on which dynamic coalition formation can stabilize quickly. Maybe surprisingly, polynomial-time con-vergence can be achieved if and only if coalition formation is based on complete or star graphs.

Coalition formation provides a versatile framework for ana-lyzing cooperative behavior in multi-agent systems. In par-ticular, hedonic coalition formation has gained considerable attention in the literature. An interesting class of hedonic games recently introduced by Aziz et al. [3] are fractional hedonic games. In these games, the utility an agent assigns to a coalition is his average valuation for the members of his coalition. Three common notions of stability in hedo-nic games are core stability, Nash stability, and individual stability. For each of these notions we show that stable par-titions may fail to exist in fractional hedonic games. For core stable partitions this holds even when all players only have symmetric zero/one valuations (“mutual friendship”). We then leverage these counter-examples to show that de-ciding the existence of stable partitions (and therefore also computing stable partitions) is NP-hard for all considered stability notions. Moreover, we show that checking whether the valuation functions of a fractional hedonic game induce strict preferences over coalitions is coNP-complete. Categories and Subject Descriptors [Theory of computation]: Algorithmic game theory; [Theory of computation]: Solution concepts in game theory; [Theory of computation]: Computational com-plexity and cryptography; [Computing methodologies]: Multi-agent systems; [Mathematics of computing]: Graph theory

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We consider the computational complexity of com-puting welfare maximizing partitions for fractional hedonic games—a natural class of coalition forma-tion games that can be succinctly represented by a graph. For such games, welfare maximizing par-titions constitute desirable ways to cluster the ver-tices of the graph. We present both intractability results and approximation algorithms for comput-ing welfare maximizing partitions. 1

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duesseldorf.de We propose a new representation setting for hedonic games, where each agent partitions the set of other agents into friends, enemies, and neutral agents, with friends and enemies being ranked. Under the assumption that preferences are monotonic (respectively, anti-monotonic) with respect to the addition of friends (respectively, en-emies), we propose a bipolar extension of the Bossong–Schweigert extension principle, and use this principle to derive the (partial) preferences of agents over coalitions. Then, for a number of solu-tion concepts, we characterize partitions that necessarily (respec-tively, possibly) satisfy them, and identify the computational com-plexity of the associated decision problems. Alternatively, we sug-gest cardinal comparability functions in order to extend to com-plete preference orders consistent with the generalized Bossong– Schweigert order.