Hedonic Coalition Formation Game Research Articles

Anonymous and Separable Hedonic Coalition Formation Games: Nash Stability Under Different Membership Rights

Anonymous and Separable Hedonic Coalition Formation Games: Nash Stability Under Different Membership Rights

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.

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

INTERNAL STABILITY AND PARETO OPTIMALITY IN HEDONIC COALITION FORMATION GAMES

We study hedonic coalition formation games that consist of a finite set of agents and a list of agents’ preferences such that each agent’s preferences depend only on the members of her coalition. An outcome of a hedonic coalition formation game is a partition (i.e., coalition structure) of the finite set of agents. We study the existence of partitions that are both internally stable and Pareto optimal. We construct an algorithm that terminates for each given hedonic coalition formation game such that the outcome of the algorithm is internally stable and Pareto optimal. We also show that if the outcome of the algorithm is the partition that consists of singleton coalitions then it is also core stable and if it is the partition that contains only the grand coalition then it is also both core stable and Nash stable.

Farsighted Rationality in Hedonic Games

We consider a hedonic coalition formation game in which a coalition chooses for each partition of the player set the probability with which it forms and thereby destroys the current partition. These probabilities are commonly known so that farsighted players know at every partition what future partitions, and hence payoffs, will be reached with what probability. Thus, players can make rational decisions about the moves they support. We show that if coalitions make mistakes with small but positive probability, then there is a behavior profile in which no coalition has a profitable one-shot deviation.

A coalitional security game against data integrity attacks in autonomous vehicle networks

Autonomous Vehicles (AV) possess an automated driving system that allows the vehicle to respond to external conditions and provide advanced and intelligent transportation services with limited to no human intervention. For AV, the legitimacy and reliability of sensed and transmitted data have direct influence on road network operations. For instance, the integrity of vehicle communications is vulnerable to various threats such as spoofing attacks. Due to the extremely volatile nature of AV, traditional centralized security solutions lack in flexibility and mobility support. Moreover, the very large scale of future AV networks mandates an innovative design of intelligent communications among the vehicles to identify authentic traffic information broadcasted all across the network. In this paper, we design a vehicular collaboration framework that drives the interactions among autonomous vehicles based on trustworthy communications to prevent data integrity attacks. The design involves a distributed, hedonic coalition formation game in which the vehicles evaluate their utilities according to their trust in each other and the data they transmit. The proposed vehicular coalition formation algorithm enables the vehicles to dynamically join and leave the collaborative communities based on trust updates. Vehicles' hybrid trust relationships are derived by integrating the three parameters of the REK model: Reputation, Experience, and Knowledge to optimally exploit the available information in the network and adapt the framework to different road traffic contexts. Furthermore, to protect the formed coalitions against data integrity attacks, a trust-based data aggregation procedure using Dempster-Shafer theory of evidence is adopted to limit the effect of false events on vehicles' decisions. The experimental results show that our collaboration framework is resilient to data corruption and fabrication attacks.

Multi-agent Reinforcement Learning for Decentralized Coalition Formation Games

We study the application of multi-agent reinforcement learning for game-theoretical problems. In particular, we are interested in coalition formation problems and their variants such as hedonic coalition formation games (also called hedonic games), matching (a common type of hedonic game), and coalition formation for task allocation. We consider decentralized multi-agent systems where autonomous agents inhabit an environment without any prior knowledge of other agents or the system. We also consider spatial formulations of these problems. Most of the literature for coalition formation problems does not consider these formulations of the problems because it increases computational complexity significantly. We propose novel decentralized heuristic learning and multi-agent reinforcement learning (MARL) approaches to train agents, and we use game-theoretic evaluation criteria such as optimality, stability, and indices like Shapley value.

Dynamics in matching and coalition formation games with structural constraints

Matching and coalition formation are fundamental aspects in the organization of many multi-agent systems. In large populations, the emergence of coalitions is often restricted by structural constraints under which agents can reorganize, e.g., local visibility or externality constraints among the agents. We study this aspect using a novel framework for dynamics with constraints within the popular domain of hedonic coalition formation games. We analyze the effects of structural constraints on the convergence of matching and coalition formation processes to stable states. Our main result are tight characterizations for the constraint structures based on which dynamic coalition formation can stabilize quickly. We show a variety of convergence results for matching and coalition formation games with different forms of locality and externality constraints. In particular, we propose and analyze a new model of graph-based visibility for coalition formation games and tightly characterize the graph structures that allow polynomial-time convergence – it can be achieved if and only if coalition formation is based on complete or star graphs.

Throughput-efficient coalition formation of selfish/altruistic nodes in ad hoc networks: a hedonic game approach

In this paper, we analyze the problem of throughput-efficient distributed coalition formation (CF) of selfish/altruistic nodes in ad hoc radio networks. We formulate the problem as a hedonic CF game with non-transferable utility and propose different preference relations (CF rules) based on individual/group rate improvement of distributed nodes. We develop a hedonic CF algorithm, through which distributed nodes may self-organize into stable throughput-efficient disjoint coalitions. We apply the concept of frequency reuse over different coalitions, such that the members of each coalition will transmit over orthogonal sub-bands with the available spectrum being optimally allocated among them. We study the computational complexity and convergence properties of the proposed hedonic CF algorithm under selfish and altruistic preferences, and present means to guarantee Nash-stability. In addition, we identify the scenarios in which a CF process might lead to instability (CF cycle), and we propose methods to avoid cycles and define different exit procedures if a CF cycle is inevitable. Performance analysis shows that the proposed algorithm with optimal bandwidth allocation provides a substantial gain, in terms of average payoff per link, over existing coalition formation algorithms for a wide SNR range.

Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities

We consider hedonic coalition formation games with variable sets of agents and extend the properties competition sensitivity and resource sensitivity (introduced by Klaus, Games Econ Behav 72:172–186, 2011, for roommate markets) to hedonic coalition formation games. Then, we show that on the domain of solvable hedonic coalition formation games, the Core is characterized by coalitional unanimity and Maskin monotonicity (see also Takamiya, Maskin monotonic coalition formation rules respecting group rights. Niigata University, Mimeo, 2010, Theorem 1). Next, we characterize the Core for solvable hedonic coalition formation games by unanimity, Maskin monotonicity, and either competition sensitivity or resource sensitivity (Corollary 2). Finally, and in contrast to roommate markets, we show that on the domain of solvable hedonic coalition formation games, there exists a solution not equal to the Core that satisfies coalitional unanimity, consistency, competition sensitivity, and resource sensitivity (Example 2).

Community detection based on strong Nash stable graph partition

The modern science of network mining has brought significant advances to the understanding of complex social networks by studying the modular structures of the networks. The problem of identifying the network modules, also called communities, is an active area of research across several disciplines due to its potential value in real-life applications. The mainstream approach for community detection generally focuses on optimization of a global metric that measures the quality of a partition over a given network. Optimizing a global metric is akin to community assignment by a centralized decision maker. However, communities in a social network often evolve in a decentralized fashion. To model the natural formation of a community, we propose a game theory-based framework treating each node as a player of a hedonic coalition formation game. We propose a novel preference relation for the players based on the players’ preference to form stable and dense community structures. The notion of strong Nash stability is used, for the first time, to determine the outcome of the coalition formation game in the context of community detection. Subsequently, we propose a greedy algorithm to obtain the strong Nash stable partition of the game. Evaluation on the well-known synthetic benchmarks and real-world networks demonstrate the superiority of the proposed algorithm.

Dynamic Distributed Resource Sharing for Mobile D2D Communications

In this work, we propose a dynamic distributed resource sharing scheme which jointly considers mode selection, resource allocation, and power control in a unified framework for general D2D communications. First, we model the joint issue of mode selection and resource allocation as a hedonic coalition formation game, while accounting for the tradeoff between the benefits in terms of available rate and the costs in terms of the mutual interference. Moreover, we develop a coalition formation process based on the switch rule, through which each cellular user makes an individual and distributed decision to form a Nash-stable partition. Second, we view the members of each coalition as a whole, and formulate a power control problem to share the aim of maximizing the sum-rate of cellular links in this coalition. To solve this NP-hard problem with online operation, we present a power control process, which employs the local piecewise-linear approach to take a locally and separately approximate optimal outcome. Finally, we present a dynamic resource sharing algorithm, which iteratively operates the coalition formation and power control processes.

Hedonic Coalition Formation in Networks

Coalition formation is a fundamental problem in the organization 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 reorganize. We capture and study this aspect using a novel network-based model for dynamic locality within the popular framework of hedonic coalition formation games. We analyze the effects of network-based visibility and structure on the convergence of coalition formation processes to stable states. Our main result is a tight characterization of the structures based on which dynamic coalition formation can stabilize quickly. Maybe surprisingly, polynomial-time convergence can be achieved if and only if coalition formation is based on complete or star graphs.

Roles and Teams Hedonic Games

We have introduced a new model of hedonic coalition formation game, which we call Roles and Teams Hedonic Games (RTHG). In this model, agents view coalitions as compositions of available roles. An agent's utility for a partition is based upon which role she fulfills within the coalition and which roles are being fulfilled within the coalition. The major contributions of the paper include designing the RTHG model, with its corresponding stability and (NP-hard) optimization criteria, designing a heuristic partitioning algorithm and local search algorithm, implementation and testing.

Coalition formation in general apex games under monotonic power indices

An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all its subgames and investigate whether there are core stable coalitions in the induced hedonic coalition formation game. Besides several general results, in particular, we develop conditions on the game for the Shapley–Shubik index, the Banzhaf index, and the normalized Banzhaf index.

Pareto optimality in coalition formation

A minimal requirement on allocative efficiency in the social sciences is Pareto optimality. In this paper, we identify a close structural connection between Pareto optimality and perfection that has various algorithmic consequences for coalition formation. Based on this insight, we formulate the Preference Refinement Algorithm (PRA) which computes an individually rational and Pareto optimal outcome in hedonic coalition formation games. Our approach also leads to various results for specific classes of hedonic games. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games, anonymous games, three-cyclic games, room-roommate games and B-hedonic games is intractable while both problems are tractable for roommate games, W-hedonic games, and house allocation with existing tenants.

Two hardness results for core stability in hedonic coalition formation games

We establish NP-completeness of two problems on core stable coalitions in hedonic games. In the first problem every player has only two acceptable coalitions in his preference list, and in the second problem the preference structures arise from the distances in an underlying metric space.

Hedonic Coalition Formation Game for Cooperative Spectrum Sensing and Channel Access in Cognitive Radio Networks

Cooperative spectrum sensing is an effective technique to improve the sensing performance and increase the spectrum efficiency in cognitive radio networks (CRNs). In this paper, we consider a CRN with multiple primary users (PUs) and multiple secondary users (SUs). We first propose a cooperative spectrum sensing and access (CSSA) scheme for all the SUs, where the SUs cooperatively sense the licensed channels of the PUs in the sensing subframe. If a channel is determined to be idle, the SUs which have sensed that channel will have a chance to transmit packets in the data transmission subframe. We then formulate this multi-channel spectrum sensing and channel access problem as a hedonic coalition formation game, where a coalition corresponds to the SUs that have chosen to sense and access a particular channel. The value function of each coalition and the utility function of each SU take into account both the sensing accuracy and the energy consumption. We propose an algorithm for decision node selection in a coalition. Moreover, we propose an algorithm based on the switch rule to allow the SUs to make decisions on whether to join or leave a coalition. We prove analytically that the set with all the SUs converges to a final network partition, which is both Nash-stable and individually stable. Besides, the proposed algorithms are adaptive to changes in network conditions. Simulation results show that our proposed CSSA scheme achieves a better performance than the closest PU (CPU) scheme and the noncooperative spectrum sensing and access (NSSA) scheme in terms of the average utility of the SUs.

A hardness result for core stability in additive hedonic games

We investigate the computational complexity of a decision problem in hedonic coalition formation games. We prove that core stability in additive hedonic games is complete for the second level of the polynomial hierarchy.

Coalition Formation in Generalized Apex Games

The class of games with one apex player is generalized to the class of games with a collection of apex sets. These simple games, together with a power index, canonically induce a hedonic coalition formation game. A monotonicity property of solutions is introduced and its meaning for the induced hedonic game is analyzed. Necessary and sufficient conditions for the existence of core stable partitions are stated and core stable partitions are characterized.