Optimal Partitions in Additively Separable Hedonic Games

We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitarian social welfare or one which is both Pareto optimal and individually rational is NP-hard. We also prove that checking whether there exists a partition which is both Pareto optimal and envy-free is $\Sigma_{2}^{p}$-complete. Even though an envy-free partition and a Nash stable partition are both guaranteed to exist for symmetric preferences, checking whether there exists a partition which is both envy-free and Nash stable is NP-complete.Comment: 11 pages; A preliminary version of this work was invited for presentation in the session `Cooperative Games and Combinatorial Optimization' at the 24th European Conference on Operational Research (EURO 2010) in Lisbo

Hedonic Games with Graph-restricted Communication

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the complexity of finding stable outcomes in such games, for several notions of stability. In particular, we provide an efficient algorithm that finds an individually stable partition for an arbitrary hedonic game on an acyclic graph. We also introduce a new stability concept -in-neighbor stability- which is tailored for our setting. We show that the problem of finding an in-neighbor stable outcome admits a polynomial-time algorithm if the underlying graph is a path, but is NP-hard for arbitrary trees even for additively separable hedonic games; for symmetric additively separable games we obtain a PLS-hardness result

Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games

Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the existence and structure of stable outcomes (i.e., partitions in coalitions), assuming that preferences are given. However, there is little discussion on this assumption. In fact, agents receive different utilities if they belong to different partitions, and thus it is natural for them to declare their preferences strategically in order to maximize their benefit. In this paper we consider strategyproof mechanisms for additively separable hedonic games and fractional hedonic games, that is, partitioning methods without payments such that utility maximizing agents have no incentive to lie about their true preferences. We focus on social welfare maximization and provide several lower and upper bounds on the performance achievable by strategyproof mechanisms for general and specific additive functions. In most of the cases we provide tight or asymptotically tight results. All our mechanisms are simple and can be computed in polynomial time. Moreover, all the lower bounds are unconditional, that is, they do not rely on any computational or complexity assumptions

Role Based Hedonic Games

In the hedonic coalition formation game model Roles Based Hedonic Games (RBHG), agents view teams as compositions of available roles. An agent\u27s utility for a partition is based upon which role she fulfills within the coalition and which additional roles are being fulfilled within the coalition. I consider optimization and stability problems for settings with variable power on the part of the central authority and on the part of the agents. I prove several of these problems to be NP-complete or coNP-complete. I introduce heuristic methods for approximating solutions for a variety of these hard problems. I validate heuristics on real-world data scraped from League of Legends games