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

Cooperative Games with Bounded Dependency Degree

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.Comment: 10 pages, full version of accepted AAAI-18 pape

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

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

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