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Worstcase equilibria
 IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1999
"... In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a ver ..."
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Cited by 851 (17 self)
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In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.
How bad is selfish routing?
 JOURNAL OF THE ACM
, 2002
"... We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route t ..."
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Cited by 678 (27 self)
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We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimumlatency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total
Coalitional Game Theory for Communication Networks: A Tutorial
 IEEE SIGNAL PROCESSING MAGAZINE
"... 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 selforganizing, decentralized, and autonomic networks, it has become imperative to seek suitabl ..."
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Cited by 50 (11 self)
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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 selforganizing, 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 applicationoriented 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 stateoftheart 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.
A Survey of Algorithms for Calculating Power Indices of Weighted Majority Games
 J. Oper. Res. Soc. Japan
, 2000
"... This paper deals with the weighted majority game, which is a familiar example of voting systems. In 1960s, U.S. Supreme Court handed down a series of "one person one vote" decisions. After that, calculations of power indices using real data were carried out and presented as evidence in the ..."
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Cited by 48 (0 self)
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This paper deals with the weighted majority game, which is a familiar example of voting systems. In 1960s, U.S. Supreme Court handed down a series of "one person one vote" decisions. After that, calculations of power indices using real data were carried out and presented as evidence in the courtroom. For example, the courts in New York State have accepted the Banzhaf index (also called the Coleman value or Chow parameters) as an appropriate measure for weighted voting systems. The calculation normally requires the aid of a computer and so many counties in U.S. hire specialized consultants, mathematicians or computer scientists (see [13]). 1 In this paper, we discuss some algorithms for calculating power indices. In Section 2, we define weighted majority games and related concepts. Section 3 defines three power indices, the ShapleyShubik power index, the Banzhaf index and the DeeganPackel index. Section 4 shows complexity classes of the problems for calculating power indices
Internet pricing with a game theoretical approach: Concepts and examples
 IEEE/ACM Trans. Netw
, 2002
"... Abstract—The basic concepts of three branches of game theory, leader–follower, cooperative, and twoperson nonzero sum games, are reviewed and applied to the study of the Internet pricing issue. In particular, we emphasize that the cooperative game (also called the bargaining problem) provides an ov ..."
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Cited by 47 (1 self)
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Abstract—The basic concepts of three branches of game theory, leader–follower, cooperative, and twoperson nonzero sum games, are reviewed and applied to the study of the Internet pricing issue. In particular, we emphasize that the cooperative game (also called the bargaining problem) provides an overall picture for the issue. With a simple model for Internet quality of service (QoS), we demonstrate that the leader–follower game may lead to a solution that is not Pareto optimal and in some cases may be “unfair,” and that the cooperative game may provide a better solution for both the Internet service provider (ISP) and the user. The practical implication of the results is that government regulation or arbitration may be helpful. The QoS model is also applied to study the competition between two ISPs, and we find a Nash equilibrium point from which the two ISPs would not move out without cooperation. The proposed approaches can be applied to other Internet pricing problems such as the Paris Metro pricing scheme. Index Terms—Bargaining problems, cooperative games, leader–follower games, quality of services, Paris Metro pricing, twoperson nonzero sum games.
Coalition games with cooperative transmission: A cure for the curse of boundary nodes in selfish packetforwarding wireless networks
 IEEE Trans. Comm
, 2009
"... Abstract — In wireless packetforwarding networks with selfish nodes, applications of a repeated game can induce the nodes to forward each others ’ packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the ..."
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Cited by 41 (7 self)
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Abstract — In wireless packetforwarding networks with selfish nodes, applications of a repeated game can induce the nodes to forward each others ’ packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the other nodes do not depend on them. This problem is sometimes known as the curse of the boundary nodes. To overcome this problem, an approach based on coalition games is proposed, in which the boundary nodes can use cooperative transmission to help the backbone nodes in the middle of the network. In return, the backbone nodes are willing to forward the boundary nodes’ packets. The stability of the coalitions is studied using the concept of a core. Then two types of fairness, namely, the minmax fairness using nucleolus and the average fairness using the Shapley function are investigated. Finally, a protocol is designed using both repeated games and coalition games. Simulation results show how boundary nodes and backbone nodes form coalitions together according to different fairness criteria. The proposed protocol can improve the network connectivity by about 50%, compared with pure repeated game schemes. I.
Nash Equilibrium and Decentralized Negotiation in Auctioning Divisible Resources
, 2003
"... We consider the problem of software agents being used as proxies for the procurement of computational and network resources. Mechanisms such as singlegood auctions and combinatorial auctions are not applicable for the management of these services, as assigning an entire resource to a single agent i ..."
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Cited by 38 (3 self)
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We consider the problem of software agents being used as proxies for the procurement of computational and network resources. Mechanisms such as singlegood auctions and combinatorial auctions are not applicable for the management of these services, as assigning an entire resource to a single agent is often undesirable and appropriate bundle sizes are difficult to determine. We investigate a divisible auction that is proportionally fair. By introducing the notion of price and demand functions that characterize optimal response functions of the bidders, we are able to prove that this mechanism has a unique Nash equilibrium for an arbitrary number of agents with heterogeneous quasilinear utilities. We also describe decentralized negotiation strategies which, with appropriate relaxation, converge locally to the equilibrium point. Given an agent with a sequence of jobs, we show how our analysis holds for a wide variety of objectives.
Optimal Routing Control: Repeated Game Approach
 IEEE Transactions on Automatic Control
, 2002
"... Communication networks shared by selfish users are considered and modeled as nonco operative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a Nash equilibrium point (NEP) that achieves the sys ..."
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Cited by 28 (1 self)
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Communication networks shared by selfish users are considered and modeled as nonco operative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a Nash equilibrium point (NEP) that achieves the systemwide optimum cost. The existence of a subgame perfect NEP that not only achieves the systemwide optimum cost but also yields a cost for each user no greater than its stage game NEP cost is shown for twonode multiple link networks. It is shown that more general networks where all users have the same sourcedestination pair have a subgameperfect NEP that achieves the minimum total system cost, under a mild technical condition. It is shown that general networks with users having multiple sourcedestination pairs do not necessarily have such an NEP.
Optimal Routing Control: Game Theoretic Approach
, 1997
"... Communication networks shared by selfish users are considered and modeled as noncooperative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a NEP that achieves the systemwide optimal cost. The exi ..."
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Cited by 26 (0 self)
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Communication networks shared by selfish users are considered and modeled as noncooperative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a NEP that achieves the systemwide optimal cost. The existence of a NEP that not only achieves the systemwide optimal cost but also yields a cost for each user no greater than its stage game NEP cost is shown for twonode multiple link networks. It is shown that more general networks where all users have the same sourcedestination pair have a NEP that achieves the minimum total system cost under a mild technical condition. It is shown general networks with users having multiple sourcedestination pairs don't necessarily have such an NEP.
Analyzing the vulnerability of critical infrastructure to attack and planning defenses
 Tutorials in Operations Research. INFORMS
, 2005
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