Algorithmic Issues in Coalitional and Dynamic Network Games

Dynamic Games and Applications, 2015

We introduce the concept of evolutionary coalitional games played in a large population. The members of the population play a strategy chosen from a finite set and interact in randomly formed coalitions. The interactions are described by a multiplayer strategic game. Each coalition generates a total utility, identified with the value of the coalition, and equal to the sum of the payoffs of its all members from the multiplayer game. The total utility is distributed among the coalition members, proportionally to their Shapley values. Evolution of the whole population is governed by the replicator equations. Polymorphic stationary states of the population are studied for various types of the multiplayer social dilemma games. It is argued that application of coalitional game theory solution concepts to social dilemma models of evolutionary game theory can foster cooperation in the long run.

2009

Coalitional network games are real-valued functions defined on a set of play-ers (the society) organized into a network and a coalition structure. The network specifies the nature of the relationship each individual has with the other individ-uals and the coalition structure specifies a collection of groups among the society. Coalitional network games model situations where the total productive value of a network among players depends on the players ’ group membership. These games thus capture the public good aspect of bilateral cooperation, i.e., network games with externalities. After studying the specific structure of coalitional networks, we propose an allocation rule under the perspective that players can alter the coalitional network structure. This means that the value of all potential alternative coalitional networks can and should influence the allocation of value among players in any given coalitional network structure. JEL classification: A14, C70.

2008 3rd International Symposium on Communications, Control and Signal Processing, 2008

We develop a unifying analytical and optimizationbased framework for the design, operation and performance evaluation of networks of dynamic autonomous agents. The fundamental view is that agents in such a network are dynamic entities that collaborate because via collaboration they can accomplish objectives and goals much better than working alone, or even accomplish objectives that they cannot achieve alone at all. Yet the benefits derived from such collaboration require some costs (e.g. communications), or equivalently, the collaboration is subject to constraints. Understanding and quantifying this tradeoff between the benefits vs the costs of collaboration, leads to new methods that can be used to analyze, design and control/operate networks of agents. Although the inspiration for the framework comes from social and economic networks, the fundamental ideas and in particular the methodology of dynamic constrained coalitional games (DCCG) can unify many concepts and algorithms for networks in various areas: social networks, communication networks, sensor networks, economic networks, biological networks, physics networks. We then analyze a specific instance of such tradeoffs arising in the design of security aware network protocols. We extend network utility maximization (NUM) so as to encompass security metrics such as "trust". The trust values assigned to nodes are based on interaction history and community-based monitoring. The effect of these trust values on the resulting protocols is that in routing and media access scheduling node trustworthiness is automatically considered and used. We develop a distributed algorithm for the joint physical-MAC-routing protocol design. Our extension to NUM with security concerns leads to resilient networks.

Journal of Statistical …, 2009

We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an ultimatum game in complex networks. Specifically, three types of players are considered: (a) empathetic, whose aspiration level and offer are equal, (b) pragmatic, who do not distinguish between the different roles and aim to obtain the same benefit, and (c) agents whose aspiration level and offer are independent. We analyze the asymptotic behavior of pure populations on different topologies using two kinds of strategic update rules. Natural selection, which relies on replicator dynamics, and Social Penalty, inspired in the Bak-Sneppen dynamics, in which players are subjected to a social selection rule penalizing not only the less fitted individuals, but also their first neighbors. We discuss the emergence of fairness in the different settings and network topologies.

The emergence of complex networks from evolutionary games is studied occurring when agents are allowed to switch interaction partners. For this purpose a coevolutionary iterated Prisoner's Dilemma game is defined on a random network with agents as nodes and games along the links. The agents change their neighborhoods to improve their payoff. The system relaxes to stationary states corresponding to cooperative Nash equilibria with the additional property that no agent can improve its payoff by changing its neighborhood. Small perturbations of the system lead to avalanches of strategy readjustments reestablishing equilibrium. As a result of the dynamics, the network of interactions develops non-trivial topological properties as a broad degree distribution suggesting scale-free behavior, small-world characteristics, and assortative mixing.

Social networks are the substrate upon which we make and evaluate many of our daily decisions: our costs and benefits depend on whether-or how many of, or which of-our friends are willing to go to that restaurant, choose that cellular provider, already own that gaming platform. Much of the research on the "diffusion of innovation," for example, takes a gametheoretic perspective on strategic decisions made by people embedded in a social context. Indeed, multiplayer games played on social networks, where the network's nodes correspond to the game's players, have proven to be fruitful models of many natural scenarios involving strategic interaction. In this paper, we embark on a mathematical and general exploration of the relationship between two-person strategic interactions (a "base game") and a "networked" version of that same game. We formulate a generic mechanism for superimposing a symmetric two-player base game M on a social network G: each node of G chooses a single strategy from M and simultaneously plays that strategy against each of its neighbors in G, receiving as its payoff the sum of the payoffs from playing M against each neighbor. We denote the networked game that results by M ⊕ G. We are broadly interested in the relationship between properties of M and of M ⊕ G: how does the character of strategic interaction change when it is embedded in a social network? We focus on two particular properties: the (pure) price of anarchy and the existence of pure Nash equilibria. We show tight results on the relationship between the price of anarchy in M and M ⊕ G in coordination games. We also show that, with some exceptions when G is bipartite, the existence or absence of pure Nash equilibria (and even the guaranteed convergence of best-response dynamics) in M and M ⊕G are not entailed in either direction. Taken together, these results suggest that the process of superimposing M on a graph is a nontrivial operation that can have rich, but bounded, effects on the strategic environment.

Arxiv preprint arXiv:1108.4115, 2011

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players involved. We present an Integer Program that calculates the price of anarchy of this game by finding the worst stable graph and the best coordinated graph for this game. We simulate the formation of the network and calculated the simulated price of anarchy, which we find tends to be rather low.

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.

Handbook of Applied Algorithms, 2008

Most of the existing and foreseen complex networks, such as the Internet, are operated and built by thousands of large and small entities (autonomous agents), which collaborate to process and deliver end-to-end flows originating from and terminating at any of them. The distributed nature of the Internet implies a lack of coordination among its users. Instead, each user attempts to obtain maximum performance according to his own parameters and objectives.

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.