Basics of coalitional games with applications to communications and networking

Game theory is the study of decision making in an interactive environment. Coalitional games fulfill the promise of group efficient solutions to problems involving strategic actions. Formulation of optimal player behavior is a fundamental element in this theory. This paper comprises a self-instructive didactic means to study basics of coalitional games indicating how coalitional game theory tools can provide a framework to tackle different problems in communications and networking. We show that coalitional game approaches achieve an improved performance compare to non-cooperative game theoretical solutions

A Logic-Based Representation for Coalitional Games with Externalities

We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other co-existing coalitions. Although externalities play a key role in many real-life situations, very little attention has been given to this issue in the multi-agent system literature, especially with regard to the computational aspects involved. To this end, we propose a new representation which, in the spirit of Ieong and Shoham [9], is based on Boolean expressions. The idea behind our representation is to construct much richer expressions that allow for capturing externalities induced upon coalitions. We show that the new representation is fully expressive, at least as concise as the conventional partition function game representation and, for many games, exponentially more concise. We evaluate the efficiency of our new representation by considering the problem of computing the Extended and Generalized Shapley value, a powerful extension of the conventional Shapley value to games with externalities. We show that by using our new representation, the Extended and Generalized Shapley value, which has not been studied in the computer science literature to date, can be computed in time linear in the size of the input

Cooperative decision making in a stochastic environment

Abstract: Cooperative game theory is a mathematical tool to analyze situations involving several individuals who can obtain certain benefits by cooperating. The main questions this theory addresses are who will cooperate with whom and how will the corresponding benefits be divided. Most results of cooperative game theory, however, only apply to cases where these benefits are deterministic. In this thesis we abandon this assumption and allow for stochastic benefits. Examples of such situations can be found in linear production situations, sequencing and financial markets. The aim of this work is then to develop a theory on games with stochastic payoffs using traditional game theory as a guideline

Network Bargaining: Creating Stability Using Blocking Sets

Bargaining theory seeks to answer the question of how to divide a jointly generated surplus between multiple agents. John Nash proposed the Nash Bargaining Solution to answer this question for the special case of two agents. Kleinberg and Tardos extended this idea to network games, and introduced a model they call the Bargaining Game. They search for surplus divisions with a notion of fairness, defined as balanced solutions, that follow the Nash Bargaining Solution for all contracting agents. Unfortunately, many networks exist where no balanced solution can be found, which we call unstable. In this thesis, we explore methods of changing unstable network structures to find fair bargaining solutions. We define the concept of Blocking Sets, introduced by Biro, Kern and Paulusma, and use them to create stability. We show that by removing a blocking set from an unstable network, we can find a balanced bargaining division in polynomial time. This motivates the search for minimal blocking sets. Unfortunately this problem is NP-hard, and hence no known efficient algorithm exists for solving it. To overcome this hardness, we consider the problem when restricted to special graph classes. We introduce a O(1)-factor approximation algorithm for the problem on planar graphs with unit edge weights. We then provide an algorithm to solve the problem optimally in graphs of bounded treewidth, which generalize trees

Finding Core Members of a Hedonic Game

Agent-based modeling (ABM) is a frequently used paradigm for social simulation; however, there is little evidence of its use in strategic coalition formations. There are few models that explore coalition formation and even fewer that validate their results against an expected outcome. Cooperative game theory is often used to study strategic coalition formation but solving games involving a significant number of agents is computationally intractable. However, there is a natural linkage between ABM and the study of strategic coalition formation. A foundational feature of ABM is the interaction of agents and their environment. Coalition formation is primarily the result of interactions between agents to form collective groups. The ABM paradigm provides a platform in which simple rules and interactions between agents can produce a macro level effect without large computational requirements. This research proposes a hybrid model combining Agent-based modeling and cooperative game theory to find members of a cooperative game’s solution. The algorithm will be applied to the core solution of hedonic games. The core solution is the most common solution set. Hedonic games are a subset of cooperative games whereby agents’ utilities are defined solely by a preference relation over the coalitions of which they are members. The utility of an agent is non-transferrable; there can be no transfer, wholly or in part, of the utility of one agent to another. Determining the core of a hedonic game is NP-complete. The heuristic algorithm utilizes the stochastic nature of ABM interactions to minimize computational complexity. The algorithm has seven coalition formation functions. Each function randomly selects agents to create new coalitions; if the new coalition improves the utility of the agents, it is incorporated into the coalition structure otherwise it is discarded. This approach reduces the computational requirements. This work contributes to the modeling and simulation body of knowledge by providing researchers with a generalized ABM algorithm for forming strategic coalition structures. It provides an empirically validated model based on existing theory that utilizes sound mathematics to reduce the computational complexity and demonstrates the advantages of combining strategic, analytical models with Agent-based models for the study of coalition formation

Cooperative Game Theory and its Insurance Applications

This survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five examples, including three insurance applications, are progressively developed throughout the paper. The characteristic function, the core, the stable sets, the Shapley value, the Nash and Kalai-Smorodinsky solutions are defined and computed for the different examples

Enabling the freight traffic controller for collaborative multi-drop urban logistics: practical and theoretical challenges

There is increasing interest in how horizontal collaboration between parcel carriers might help alleviate problems associated with last-mile logistics in congested urban centers. Through a detailed review of the literature on parcel logistics pertaining to collaboration, along with practical insights from carriers operating in the United Kingdom, this paper examines the challenges that will be faced in optimizing multicarrier, multidrop collection, and delivery schedules. A “freight traffic controller” (FTC) concept is proposed. The FTC would be a trusted third party, assigned to equitably manage the work allocation between collaborating carriers and the passage of vehicles over the last mile when joint benefits to the parties could be achieved. Creating this FTC concept required a combinatorial optimization approach for evaluation of the many combinations of hub locations, network configuration, and routing options for vehicle or walking to find the true value of each potential collaboration. At the same time, the traffic, social, and environmental impacts of these activities had to be considered. Cooperative game theory is a way to investigate the formation of collaborations (or coalitions), and the analysis used in this study identified a significant shortfall in current applications of this theory to last-mile parcel logistics. Application of theory to urban freight logistics has, thus far, failed to account for critical concerns including (a) the mismatch of vehicle parking locations relative to actual delivery addresses; (b) the combination of deliveries with collections, requests for the latter often being received in real time during the round; and (c) the variability in travel times and route options attributable to traffic and road network conditions

Cooperation and allocation

This thesis deals with various models of cooperation, including games with transferable utility, games with nontransferable utility, bankruptcy situations, communication situations, spillover games and sequencing situations. The focus is on analysing rules for dividing the profits of cooperation. This analysis is performed in terms of properties that one might require of such an allocation mechanism. In addition, properties of the underlying situations and games are studied.

Game-Theoretic Frameworks for the Techno-Economic Aspects of Infrastructure Sharing in Current and Future Mobile Networks

RÉSUMÉ Le phénomène de partage d’infrastructure dans les réseaux mobiles a prévalu au cours des deux dernières décennies. Il a pris de l’ampleur en particulier pendant les deux dernières migrations technologiques, à savoir de la 2G à la 3G et de la 3G à la 4G et il sera encore plus crucial à très court terme avec l’avènement de la 5G. En permettant aux Opérateurs de Réseaux Mobiles (ORM) de faire face à la demande croissante des utilisateurs et à la baisse des revenus. Il n’est pas rare non plus que le partage d’infrastructure s’accompagne du partage du spectre, une ressource essentielle et de plus en plus rare pour les réseaux mobiles. Dans ce milieu, la communauté des chercheurs, parmis d’autres, a étudié les multiples aspects techniques du partage d’infrastructure parfois associés au partage du spectre. Entre autres, ces aspects techniques comprennent l’évaluation des performances en termes de métriques de réseau, de gestion de ressources et d’habilitateurs et d’architectures adaptées. Les aspects économiques ont également été abordés, mais généralement en se concentrant étroitement sur l’estimation des économies de coûts des dfférentes alternatives de partage d’infrastructure. Cependant, lorsqu’on considère le problème du partage d’infrastructure, et le cas échéant aussi du partage du spectre du point de vue d’un ORM, qui est une entité intéressée à maximiser le profit, il est important d’évaluer non seulement la réduction des coûts de cette infrastructure, et le cas échéant aussi le partage du spectre, mais aussi leur impact sur les performances du réseau et par conséquent sur les revenus de l’ORM. De ce point de vue, la viabilité du partage d’infrastructure ne doit pas être prise pour acquise ; afin d’étudier le problème stratégique d’un ORM concluant un accord de partage avec un ou plusieurs autres ORM, les aspects techniques et économiques doivent être pris en compte. Cette étude constitue le premier objectif de ce projet de recherche doctorale. Plus précisément, nous avons considéré plusieurs variantes résultant de deux cas où chaque variante a été abordée par un modèle mathématique approprié. Ces variantes répondent à un scénario 4G commun dans lequel il existe un ensemble de ORM avec des parts de marché données qui coexistent dans une zone géographique urbaine dense ; chaque ORM doit décider s’il faut déployer une couche de petites cellules dans la zone et, le cas échéant, s’il doit le faire lui-même ou en concluant un accord de partage en créant un réseau partagé avec certains, ou la totalité, des autres ORM, auquel cas une coalition est créée. Une caractéristique commune importante de ces variantes est le modèle de tarification de l’utilisateur défini comme une fonction linéaire du taux moyen perçu par l’utilisateur en fonction de la coalition dont fait partie l’ORM de l’utilisateur.----------ABSTRACT The phenomenon of infrastructure sharing in mobile networks has been prevalent over the last two decades. It has gathered momentum especially during the last two technology migrations, i.e., from 2G to 3G and from 3G to 4G and it will be even more crucial with the advent of 5G. The key rationale behind such phenomenon is cost reduction as a means for Mobile Network Operators (MNOs) to deal with an increasing user demand but declining revenues. It is also not unusual for infrastructure sharing to go hand in hand with sharing of spectrum, an essential and increasingly scarce resource for mobile networks. In this milieu, the research community (but not only) has addressed multiple technical aspects of infrastructure sharing sometimes combined with spectrum sharing. Among others, such technical aspects include performance evaluation in terms of network metrics, resource management and enablers and adapted architectures. Economic aspects have been addressed as well, but usually with a narrow focus on estimating the cost savings of the di˙erent infrastructure sharing alternatives. However, from the perspective of an MNO, which is a self-interested, profit-maximizing entity, it is important to assess not only the cost reduction that infrastructure sharing, and when applicable, also spectrum sharing bring about, but also their impact on the network performance and consequently on the MNO’s revenues. From this perspective, the viability of infrastructure sharing should not be taken for granted; in order to study the strategic problem of an MNO entering a sharing agreement with one or multiple other MNOs, both technical and economic aspects should be taken into account – such study has been the first objective of this doctoral research project. We have specifically considered multiple variants arising from two cases where each variant has been tackled by an appropriate mathematical model. These variants address a common 4G scenario in which there is a set of MNOs with given market shares that coexist in a given dense urban geographical area; each MNO has to decide whether to deploy a layer of small cells in the area and if so, whether to do that by itself or by entering a sharing agreement, i.e., building a shared network with a subset or all other MNOs (in which case a coalition is created). One key common feature of these variants is the user pricing model which is defined as a linear function of the average rate perceived by the user depending on the coalition joined by the user’s MNO; such pricing model allows us to capture the impact that infrastructure sharing, and, when applicable, also spectrum sharing have on the MNO’s revenues through a network performance metric. In turn, the two key outcomes of the models tackling these variants are the set of coalitions and the number of small cells they deploy