Hedonic Games Research Articles

The complexity of verifying popularity and strict popularity in altruistic hedonic games

We consider average- and min-based altruistic hedonic games and study the problem of verifying popular and strictly popular coalition structures. While strict popularity verification has been shown to be coNP-complete in min-based altruistic hedonic games, this problem has been open for equal- and altruistic-treatment average-based altruistic hedonic games. We solve these two open cases of strict popularity verification and then provide the first complexity results for popularity verification in (average- and min-based) altruistic hedonic games, where we cover all three degrees of altruism.

Envy-freeness in 3D hedonic games

We study the problem of fairly partitioning a set of agents into coalitions based on the agents’ additively separable preferences, which can also be viewed as a hedonic game. We study three successively weaker solution concepts, related to envy, weakly justified envy, and justified envy. In a model in which coalitions may have any size, trivial solutions exist for these concepts, which provides a strong motivation for placing restrictions on coalition size. In this paper, we require feasible coalitions to have size three. We study the existence of partitions that are envy-free, weakly justified envy-free, and justified envy-free, and the computational complexity of finding such partitions, if they exist. We impose various restrictions on the agents’ preferences and present a complete complexity classification in terms of these restrictions.

Stability based on single-agent deviations in additively separable hedonic games

Coalition formation is a central concern in multiagent systems. A common desideratum for coalition structures is stability, defined by the absence of beneficial deviations of single agents. Such deviations require an agent to improve her utility by joining another coalition. On top of that, the feasibility of deviations may also be restricted by demanding consent of agents in the welcoming and/or the abandoned coalition. While most of the literature focuses on deviations constrained by unanimous consent, we also study consent decided by majority vote and introduce two new stability notions that can be seen as local variants of another solution concept called popularity. We investigate stability in additively separable hedonic games by pinpointing boundaries to computational complexity depending on the type of consent and friend-oriented utility restrictions. The latter restrictions shed new light on well-studied classes of games based on the appreciation of friends or the aversion to enemies. Many of our positive results follow from a new combinatorial observation that we call the Deviation Lemma and that we leverage to prove the convergence of simple and natural single-agent dynamics under fairly general conditions. Our negative results, in particular, resolve the complexity of contractual Nash stability in additively separable hedonic games.

Stability in Online Coalition Formation

Coalition formation is concerned with the question of how to partition a set of agents into disjoint coalitions according to their preferences. Deviating from most of the previous work, we consider an online variant of the problem, where agents arrive in sequence and whenever an agent arrives, they have to be assigned to a coalition immediately and irrevocably. The scarce existing literature on online coalition formation has focused on the objective of maximizing social welfare, a demanding requirement, even in the offline setting. Instead, we seek to achieve stable coalition structures in an online setting, and focus on stability concepts based on deviations by single agents. We present a comprehensive picture in additively separable hedonic games, leading to dichotomies, where positive results are obtained by deterministic algorithms and negative results even hold for randomized algorithms.

ELEKTRA: Empowering prosumers with distributed prosumer grouping and game-theoretic energy procurement

In this paper, the ELEKTRA framework is introduced, a novel community energy management system that organizes the prosumers into autonomous communities and determines the prosumers’ optimal energy procurement in a distributed manner. Our motivation stems from the increasing complexity of the energy procurement for prosumers and the need for more efficient and decentralized approaches to optimize their energy consumption. The first element of the ELEKTRA framework implements an autonomous hedonic game-theoretic model at the prosumers’ home energy management controllers, considering the prosumers’ individual energy consumption and generation patterns, as well as the utility-provided rewards for proactive participation. Specifically, the prosumer grouping is modeled as a hedonic game, demonstrating the existence of a Nash-stable and individually-stable prosumer grouping. The second element of the ELEKTRA framework employs a distributed non-cooperative game-theoretic approach. This addresses how prosumers strategically consume energy to meet their needs while maximizing their payoff by procuring additional energy from the utility company. Also, utilizing the theory of n-person concave games allows for a thorough evaluation of accuracy, performance, and complexity in determining optimal energy consumption for prosumers. A comprehensive evaluation of the ELEKTRA framework is conducted using real data from the southwest region of USA. The results demonstrate the operational effectiveness of the ELEKTRA framework, showcasing its superiority in optimizing prosumer payoff compared to existing models. The performance assessment, grounded in real-world data, provides valuable insights into the efficacy of the ELEKTRA framework in contrast to current state-of-the-art.

ABMSCORE: a heuristic algorithm for forming strategic coalitions in agent-based simulation

ABSTRACT Integrating human behavior into agent-based models has been challenging due to its diversity. An example is strategic coalition formation, which occurs when an individual decides to collaborate with others because it strategically benefits them, thereby increasing the expected utility of the situation. An algorithm called ABMSCORE was developed to help model strategic coalition formation in agent-based models. The ABMSCORE algorithm employs hedonic games from cooperative game theory and has been applied to various situations, including refugee egress and smallholder farming cooperatives. This paper discusses ABMSCORE, including its mechanism, requirements, limitations, and application. To demonstrate the potential of ABMSCORE, a new application example is given, which is based on a complex version of the Thomas Schelling’s segregation model. The intent of the paper is to provide the potential user with enough information so that they can apply ABMSCORE to their simulation products.

Multi-objective optimization for energy efficient cooperative communication in energy-constrained overlay Cognitive Radio Networks

With the rapid proliferation of wireless devices, energy efficiency and addressing spectrum scarcity have become critical global concerns. To address these challenges, this paper explores radio-frequency energy harvesting in Cognitive Radio Networks (CRNs) as a solution which can significantly extend the battery life of mobile devices. In this setup, energy-constrained secondary users (SUs) use Simultaneous Wireless Information and Power Transfer (SWIPT) technology to harvest energy from primary signals and aid primary transmission. We propose a joint time-switching and power-splitting technique to maximize energy harvesting, achieving a 97.7% accurate sub-optimal solution compared to the optimal (benchmark) result. Furthermore, we investigate optimal power allocation during cooperative communication and secondary transmission, resulting in a near-optimal solution with 98.5% accuracy. We also introduce a cooperative communication framework using the Hedonic game concept, enabling SUs to establish preferred partnerships with suitable primary users (PUs). Numerical results indicate that this cooperative framework enhances the secondary network’s overall utility, average SU satisfaction, and SU participation when compared to the non-cooperative approach.

A Blockchain-Based Hedonic Game Scheme for Reputable Fog Federations

A Blockchain-Based Hedonic Game Scheme for Reputable Fog Federations

Topological distance games

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs—for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.

Hedonic diversity games: A complexity picture with more than two colors

Hedonic diversity games are a variant of the classical hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as colors in the model) and provided some initial complexity-theoretic and existential results concerning Nash and individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a comprehensive parameterized-complexity picture for computing Nash and individually stable outcomes with respect to the most natural parameterizations of the problem. Crucially, our results hold for general hedonic diversity games where the number of colors is not necessarily restricted to two, and show that—apart from two trivial cases—a necessary condition for tractability in this setting is that the number of colors is bounded by the parameter. Moreover, for the special case of two colors we resolve an open question asked in previous work (Boehmer and Elkind, AAAI 2020).

On hedonic games with common ranking property

On hedonic games with common ranking property

Altruism in coalition formation games

Nguyen et al. (2016) introduced altruistic hedonic games in which agents’ utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing our model to altruistic hedonic games, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model and showing some desirable properties, we additionally study some common stability notions and provide a computational analysis of the associated verification and existence problems.

PAC Learning and Stabilizing Hedonic Games: Towards a Unifying Approach.

We study PAC learnability and PAC stabilizability of Hedonic Games (HGs), i.e., efficiently inferring preferences or core-stable partitions from samples. We first expand the known learnability/stabilizability landscape for some of the most prominent HGs classes, providing results for Friends and Enemies Games, Bottom Responsive, and Anonymous HGs. Then, having a broader view in mind, we attempt to shed light on the structural properties leading to learnability/stabilizability, or lack thereof, for specific HGs classes. Along this path, we focus on the fully expressive Hedonic Coalition Nets representation of HGs. We identify two sets of conditions that lead to efficient learnability, and which encompass all of the known positive learnability results. On the side of stability, we reveal that, while the freedom of choosing an ad hoc adversarial distribution is the most obvious hurdle to achieving PAC stability, it is not the only one. First, we show a distribution independent necessary condition for PAC stability. Then, we focus on W-games, where players have individual preferences over other players and evaluate coalitions based on the least preferred member. We prove that these games are PAC stabilizable under the class of bounded distributions, which assign positive probability mass to all coalitions. Finally, we discuss why such a result is not easily extendable to other HGs classes even in this promising scenario. Namely, we establish a purely computational property necessary for achieving PAC stability.

Complexity of Probabilistic Inference in Random Dichotomous Hedonic Games

Hedonic games model cooperative games where agents desire to form coalitions, and only care about the composition of the coalitions of which they are members. Focusing on various classes of dichotomous hedonic games, where each agent either approves or disapproves a given coalition, we propose the random extension, where players have an independent participation probability. We initiate the research on the computational complexity of computing the probability that coalitions and partitions are optimal or stable. While some cases admit efficient algorithms (e.g., agents approve only few coalitions), they become computationally hard (#P-hard) in their complementary scenario. We then investigate the distribution of coalitions in perfect partitions and their performance in majority games, where an agent approves coalitions in which the agent is friends with the majority of its members. When friendships independently form with a constant probability, we prove that the number of coalitions of size 3 converges in distribution to a Poisson random variable.

Topological Distance Games

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs—for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.

Causes of Stability in Dynamic Coalition Formation

We study the formation of stable outcomes via simple dynamics in cardinal hedonic games, where the utilities of agents change over time depending on the history of the coalition formation process. Specifically, we analyze situations where members of a coalition decrease their utility for a leaving agent (resent) or increase their utility for a joining agent (appreciation). We show that in contrast to classical dynamics, for resentful or appreciative agents, dynamics are guaranteed to converge under mild conditions for various stability concepts. Thereby, we establish that both resent and appreciation are strong stability-driving forces.

Feature Selection as a Hedonic Coalition Formation Game for Arabic Topic Detection

Arabic topic detection is a Natural Language Processing (NLP) task that aims to assign a topic or a set of topics to a new document based on its content and selected features. Feature selection is an essential topic detection technique used to capture discriminative and descriptive features in documents to enhance the performance of topic detection. This paper proposes a novel feature selection approach formulated as a Hedonic Coalition Formation Game. We use the proposed method to describe each topic with a unique Topic Oriented Vocabulary (TOV) vector. We inspect the performances of the vocabularies obtained by solving the Hedonic game in topic detection over several Arabic corpora. In addition, the proposed feature selection method is compared with a Mutual Information (MI) based vocabulary vector generation method. The reported results show the effectiveness of the proposed feature selection approach by generating new vocabularies with highly discriminating features and reduced dimensions.

Dynamic Fog Federation Scheme for Internet of Vehicles

Federated fog computing is an answer for horizontally upscaling fog resources to improve the Quality of Service (QoS) of Internet of Things (IoT) applications. However, the dynamic nature of some IoT’s crucial components, such as the ones of Internet of Vehicles (IoV), may hinder the QoS improvement and result in its deterioration instead. Specifically, delays can occur due to the unoptimized distribution of services and unbalanced network traffic loads on the fog nodes. The current federated fog architectures ignore the mobility of users during the formation of fog federations. In this work, we present an adaptive and efficient fog federation formation scheme using game theory according to the service requirements. The problem formulation in terms of forming the federations and offloading requests among fog members is formulated as an integer program, then modeled as a Hedonic game. We adopt the Merge & Split as a formation technique, where the federations that are not satisfied in terms of QoS merge with other federations that would enhance the service performance. Our adaptive fog federation formation mechanism is designed to cope with the environmental changes in the IoV paradigm. Experimental evaluation shows that our framework can acquire better QoS and lower time to form the federations compared to the literature.

Reaching Individually Stable Coalition Structures

The formal study of coalition formation in multi-agent systems is typically realized in the framework of hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this article, we study the convergence of simple dynamics leading to stable partitions in a variety of established classes of hedonic games, including anonymous, dichotomous, fractional, and hedonic diversity games. The dynamics we consider is based on individual stability: an agent will join another coalition if she is better off and no member of the welcoming coalition is worse off. Our results are threefold. First, we identify conditions for the (fast) convergence of our dynamics. To this end, we develop new techniques based on the simultaneous usage of multiple intertwined potential functions and establish a reduction uncovering a close relationship between anonymous hedonic games and hedonic diversity games. Second, we provide elaborate counterexamples determining tight boundaries for the existence of individually stable partitions. Third, we study the computational complexity of problems related to the coalition formation dynamics. In particular, we settle open problems suggested by Bogomolnaia and Jackson, Brandl et al., and Boehmer and Elkind.

Hedonic coalition formation games: Nash stability under different membership rights

Purpose - We study hedonic coalition formation games in which each agent has preferences over the coalitions she is a member of. Hedonic coalition formation games are used to model economic, social, and political instances in which people form coalitions. The outcome of a hedonic coalition formation game is a partition. We consider stability concepts of a partition that are based on a single-agent deviation under different membership rights, that is, we study Nash stability under different membership rights. We revisit the conditions that guarantee the existence of Nash stable partitions and provide examples of hedonic coalition formation games satisfying these conditions. Methodology – While analyzing a stability notion for hedonic coalition formation games, two crucial points are considered: i) who can deviate from the given partition, ii) what are the allowed movements for the deviator(s), i.e., what deviators are entitled to do. For the first point, the deviation of a single agent is considered for Nash stabilities. For the second point, the allowed movements for deviators are determined by specifying membership rights, that is, membership rights describe whose approval is needed for a particular deviation. So, we reconsider stability concepts by using membership rights based on individual deviations, i.e., we consider Nash stability under different membership rights for hedonic coalition formation games. Findings- A classification of stability concepts based on a single-agent deviation for hedonic coalition formation games are provided by employing membership rights. The conditions in the literature guaranteeing the existence of Nash stable partitions for all membership rights are revisited. For each condition, an example of a hedonic coalition formation game satisfying the condition is given. Hence, a complete analysis of sufficient conditions for all Nash stability concepts are provided. Conclusion- To choose the correct stability notion one first should understand the membership rights in the environment that she studies. Then, for hedonic coalition formation problems, the appropriate Nash stability notion consistent with the ongoing membership rights should be chosen when single-agent deviation is considered. Keywords: Coalition formation, Hedonic games, Nash stability, membership rights, separable preferences JEL Codes: C71, C78, D71