Allocation rules for coalitional network games

Games and Economic Behavior, 2005

Previous allocation rules for network games, such as the Myerson value, implicitly or explicitly take the network structure as fixed. In many situations, however, the network structure can be altered by players. This means that the value of alternative network structures (not just sub-networks) can and should influence the allocation of value among players on any given network structure. I present a family of allocation rules that incorporate information about alternative network structures when allocating value.  2004 Elsevier Inc. All rights reserved. JEL classification: A14; C71; C72; D85

IEEE Signal Processing Magazine, 2000

Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and autonomic networks, it has become imperative to seek suitable game theoretical tools that allow to analyze and study the behavior and interactions of the nodes in future communication networks. In this context, this tutorial introduces the concepts of cooperative game theory, namely coalitional games, and their potential applications in communication and wireless networks. For this purpose, we classify coalitional games into three categories: Canonical coalitional games, coalition formation games, and coalitional graph games. This new classification represents an application-oriented approach for understanding and analyzing coalitional games. For each class of coalitional games, we present the fundamental components, introduce the key properties, mathematical techniques, and solution concepts, and describe the methodologies for applying these games in several applications drawn from the state-of-the-art research in communications. In a nutshell, this article constitutes a unified treatment of coalitional game theory tailored to the demands of communications and network engineers.

2011

We propose an allocation rule that takes into account the importance of both players and their links and characterizes it for a fixed network. Unlike previous rules, our characterization does not require that the allocation rule be component balance. Next, we extend it to flexible networksà la Jackson (2005). Finally, we provide a comparison with other fixed network (Myerson and Position value) and flexible network (Player and Link Based) allocation rules through some examples. JEL classifications: A14; C71; C72; D85

2004

We study mechanisms that can be modelled as coalitional games with transferable utilities, and apply ideas from mechanism design and game theory to problems arising in a network design setting. We establish an equivalence between the game-theoretic notion of agents being substitutes and the notion of frugality of a mechanism. We characterize the core of the network design game and relate it to outcomes in a sealed bid auction with VCG payments. We show that in a game, agents are substitutes if and only if the core of the forms a complete lattice. We look at two representative games-Minimum Spanning Tree and Shortest Path-in this light.

Ieee Signal Processing Magazine Special Issue on Game Theory For Signal Processing and Communication, 2009

Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and autonomic networks, it has become imperative to seek suitable game theoretical tools that allow to analyze and study the behavior and interactions of the nodes in future communication networks. In this context, this tutorial introduces the concepts of cooperative game theory, namely coalitional games, and their potential applications in communication and wireless networks. For this purpose, we classify coalitional games into three categories: Canonical coalitional games, coalition formation games, and coalitional graph games. This new classification represents an application-oriented approach for understanding and analyzing coalitional games. For each class of coalitional games, we present the fundamental components, introduce the key properties, mathematical techniques, and solution concepts, and describe the methodologies for applying these games in several applications drawn from the state-of-the-art research in communications. In a nutshell, this article constitutes a unified treatment of coalitional game theory tailored to the demands of communications and network engineers.

We introduce the notion of a Bi-cooperative network game as a graph restricted Bi-cooperative game where interactions among players with bipolar motives are considered only through some exogenously given networks. Once such a network forms, the challenge rests on obtaining a suitable allocation of the payoff accrued by its members. In classical Network games the Position value is an important link based allocation rule. We extend this idea to define the Position value for the class of Bi-cooperative network games. It is then characterized using two axioms: efficiency (EFF) and balanced link contribution (BLC).

Ec, 2002

We study mechanisms that can be modelled as coalitional games with transferable utilities, and apply ideas from mechanism design and game theory to problems arising in a network design setting. We establish an equivalence between the game-theoretic notion of agents being substitutes and the notion of frugality of a mechanism. We characterize the core of the network design game and relate it to outcomes in a sealed bid auction with VCG payments. We show that in a game, agents are substitutes if and only if the core of the forms a complete lattice. We look at two representative games-Minimum Spanning Tree and Shortest Path-in this light.

Intelligent Agents …, 2002

In the last few years the use of coalition formation algorithms in multi-agent systems has been proposed as a possible way of modelling autonomous agent cooperation. Game theory provides different concepts for the stability of solutions in cooperative games, regarding the fairness of the resultant payment configuration. One of these is the core. In this paper we present an analysis -based upon game theory-for a class of task-oriented problems arising from some Internet transactions. A procedure that guarantees an optimum task allocation is defined, and a new payoff division model is proposed for the corresponding value. We prove that the proposed payoff division lies inside the core. The whole computation (of the optimal value and the payoffs) has a polynomial complexity in the number of agents.

A very common question appearing in resource management is: what is the optimal way of behaviour of the agents and distribution of limited resources. Is any form of cooperation more preferable strategy than pure competition? How cooperation can be treated in the game theoretic framework: just as one of a set of Pareto optimal solutions or cooperative game theory is a more promising approach? This research is based on results proving the existence of a non-empty K -core, that is, the set of allocations acceptable for the family K of all feasible coalitions, for the case when this family is a set of subtrees of a tree.

2008

Cooperative game theory is concerned primarily with groups of players who coordinate their actions and pool their winnings. One of the main concerns is how to divide the extra earnings (or cost savings) among the members of the coalitions. Thus a number of solution concepts for cooperative games have been proposed. In this chapter, a selection of basic notions and solution concepts for cooperative games are presented and analyzed in detail.