Simple Causes of Complexity in Hedonic Games

Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on expressivity of hedonic games that are sufficient for the problem of checking whether a given game admits a stable outcome to be computationally hard. Somewhat surprisingly, these conditions are very mild and intuitive. Our results apply to a wide range of stability concepts (core stability, individual stability, Nash stability, etc.) and to many known formalisms for hedonic games (additively separable games, games with W-preferences, fractional hedonic games, etc.), and unify and extend known results for these formalisms. They also have broader applicability: for several classes of hedonic games whose computational complexity has not been explored in prior work, we show that our framework immediately implies a number of hardness results for them.Comment: 7+9 pages, long version of a paper in IJCAI 201

Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences [Bredereck et al., 2019]: each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem. Moreover, for the classic setting with rooms of size two, we present a linear-time algorithm that computes an outcome that is core and exchange stable as well as Pareto optimal. Many of our results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2

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

Structure in Dichotomous Preferences

Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of this type have been obtained for the setting where each voter's preference list is a total order of candidates. The goal of this paper is to extend this line of research to the setting where voters' preferences are dichotomous, i.e., each voter approves a subset of candidates and disapproves the remaining candidates. We propose several analogues of the notions of single-peaked and single-crossing preferences for dichotomous profiles and investigate the relationships among them. We then demonstrate that for some of these notions the respective restricted domains admit efficient algorithms for computationally hard approval-based multi-winner rules.Comment: A preliminary version appeared in the proceedings of IJCAI 2015, the International Joint Conference on Artificial Intelligenc

Justified Representation in Multiwinner Voting: Axioms and Algorithms

Suppose that a group of voters wants to select k 1 alternatives from a given set, and each voter indicates which of the alternatives are acceptable to her: the alternatives could be conference submissions, applicants for a scholarship or locations for a fast food chain. In this setting it is natural to require that the winning set represents the voters fairly, in the sense that large groups of voters with similar preferences have at least some of their approved alternatives in the winning set. We describe several ways to formalize this idea, and show how to use it to classify voting rules; surprisingly, two voting rules proposed in the XIXth century turn out to play an important role in our analysis

On Parameterized Complexity of Group Activity Selection Problems on Social Networks

In Group Activity Selection Problem (GASP), players form coalitions to participate in activities and have preferences over pairs of the form (activity, group size). Recently, Igarashi et al. have initiated the study of group activity selection problems on social networks (gGASP): a group of players can engage in the same activity if the members of the group form a connected subset of the underlying communication structure. Igarashi et al. have primarily focused on Nash stable outcomes, and showed that many associated algorithmic questions are computationally hard even for very simple networks. In this paper we study the parameterized complexity of gGASP with respect to the number of activities as well as with respect to the number of players, for several solution concepts such as Nash stability, individual stability and core stability. The first parameter we consider in the number of activities. For this parameter, we propose an FPT algorithm for Nash stability for the case where the social network is acyclic and obtain a W[1]-hardness result for cliques (i.e., for classic GASP); similar results hold for individual stability. In contrast, finding a core stable outcome is hard even if the number of activities is bounded by a small constant, both for classic GASP and when the social network is a star. Another parameter we study is the number of players. While all solution concepts we consider become polynomial-time computable when this parameter is bounded by a constant, we prove W[1]-hardness results for cliques (i.e., for classic GASP).Comment: 9 pages, long version of accepted AAMAS-17 pape

Campaign Management under Approval-Driven Voting Rules

Approval-like voting rules, such as Sincere-Strategy Preference-Based Approval voting (SP-AV), the Bucklin rule (an adaptive variant of $k$-Approval voting), and the Fallback rule (an adaptive variant of SP-AV) have many desirable properties: for example, they are easy to understand and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard even if the degree to which we need to affect the votes is small. Nevertheless, we identify a large class of scenarios that admit fixed-parameter tractable algorithms.Comment: 34 pages, 1 figur

Simple Coalitional Games with Beliefs

We introduce coalitional games with beliefs (CGBs), a natural generalization of coalitional games to environments where agents possess private beliefs regarding the capabilities (or types) of others. We put forward a model to capture such agent-type uncertainty, and study coalitional stability in this setting. Specifically, we introduce a notion of the core for CGBs, both with and without coalition structures. For simple games without coalition structures, we then provide a characterization of the core that matches the one for the full information case, and use it to derive a polynomial-time algorithm to check core nonemptiness. In contrast, we demonstrate that in games with coalition structures allowing beliefs increases the computational complexity of stability-related problems. In doing so, we introduce and analyze weighted voting games with beliefs, which may be of independent interest. Finally, we discuss connections between our model and other classes of coalitional games