Abstract In this paper we introduce a capacity allocation game which models the problem of maximizing network utility from the perspective of distributed noncooperative agents. Motivated by the idea of self-managed networks, in the developed framework the decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows. An efficient decentralized algorithm is given for computing a strongly Pareto-optimal strategies, constituting a pure Nash equilibrium. Subsequently, we discuss the properties of the introduced game related to the Price of Anarchy and Price of Stability. The paper is concluded with an experimental study.
In @cite_62 coalitional games for a communication systems are considered. A classification of such games distinguishing three main types of cooperative games is given. It is stressed that the need of autonomic and self-organizing networks implies the necessity of developing distributed algorithms which enable each network device to make independent decision concerning network management. Application examples of cooperative games in computer networks, mainly wireless, are discussed. Presented arguments corroborate the game-theoretic approach as a promising solution for autonomic (and self-organizing) networks.
@cite_62
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In this tutorial, we provided a comprehensive overview of coalitional game theory, and its usage in wireless and communication networks. For this purpose, we introduced a novel classification of coalitional games by grouping the sparse literature into three distinct classes of games: canonical coalitional games, coalition formation games, and coalitional graph games. For each class, we explained in details the fundamental properties, discussed the main solution concepts, and provided an in-depth analysis of the methodologies and approaches for using these games in both game theory and communication applications. The presented applications have been carefully selected from a broad range of areas spanning a diverse number of research problems. The tutorial also sheds light on future opportunities for using the strong analytical tool of coalitional games in a number of applications. In a nutshell, this article fills a void in existing communications literature, by providing a novel tutorial on applying coalitional game theory in communication networks through comprehensive theory and technical details as well as through practical examples drawn from both game theory and communication application. Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network. We present a view of cooperative control using the language of learning in games. We review the game-theoretic concepts of potential and weakly acyclic games, and demonstrate how several cooperative control problems, such as consensus and dynamic sensor coverage, can be formulated in these settings. Motivated by this connection, we build upon game-theoretic concepts to better accommodate a broader class of cooperative control problems. In particular, we extend existing learning algorithms to accommodate restricted action sets caused by the limitations of agent capabilities and group based decision making. Furthermore, we also introduce a new class of games called sometimes weakly acyclic games for time-varying objective functions and action sets, and provide distributed algorithms for convergence to an equilibrium. Coalitional games allow subsets (coalitions) of players to cooperate to receive a collective payoff. This payoff is then distributed “fairly” among the members of that coalition according to some division scheme. Various solution concepts have been proposed as reasonable schemes for generating fair allocations. The Shapley value is one classic solution concept: player i’s share is precisely equal to i’s expected marginal contribution if the players join the coalition one at a time, in a uniformly random order. In this paper, we consider the class of supermodular games (sometimes called convex games), and give a fully polynomial-time randomized approximation scheme (FPRAS) to compute the Shapley value to within a (1 ±e) factor in monotone supermodular games. We show that this result is tight in several senses: no deterministic algorithm can approximate Shapley value as well, no randomized algorithm can do better, and both monotonicity and supermodularity are required for the existence of an efficient (1 ±e)-approximation algorithm. We also argue that, relative to supermodularity, monotonicity is a mild assumption, and we discuss how to transform supermodular games to be monotonic.