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589
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 657 (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
The price of stability for network design with fair cost allocation
 In Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS
, 2004
"... Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite differ ..."
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Cited by 281 (30 self)
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Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite different from the centrally enforced optimum. We study the quality of the best Nash equilibrium, and refer to the ratio of its cost to the optimum network cost as the price of stability. The best Nash equilibrium solution has a natural meaning of stability in this context — it is the optimal solution that can be proposed from which no user will defect. We consider the price of stability for network design with respect to one of the most widelystudied protocols for network cost allocation, in which the cost of each edge is divided equally between users whose connections make use of it; this fairdivision scheme can be derived from the Shapley value, and has a number of basic economic motivations. We show that the price of stability for network design with respect to this fair cost allocation is O(log k), where k is the number of users, and that a good Nash equilibrium can be achieved via bestresponse dynamics in which users iteratively defect from a starting solution. This establishes that the fair cost allocation protocol is in fact a useful mechanism for inducing strategic behavior to form nearoptimal equilibria. We discuss connections to the class of potential games defined by Monderer and Shapley, and extend our results to cases in which users are seeking to balance network design costs with latencies in the constructed network, with stronger results when the network has only delays and no construction costs. We also present bounds on the convergence time of bestresponse dynamics, and discuss extensions to a weighted game.
Selfish Routing and the Price of Anarchy
 MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
, 2007
"... Selfish routing is a classical mathematical model of how selfinterested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this in ..."
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Cited by 255 (11 self)
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Selfish routing is a classical mathematical model of how selfinterested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this inefficiency. We survey recent work that analyzes the price of anarchy of selfish routing. We also describe related results on bounding the worstpossible severity of a phenomenon called Braess’s Paradox, and on three techniques for reducing the price of anarchy of selfish routing. This survey concentrates on the contributions of the author’s PhD thesis, but also discusses several more recent results in the area.
Strategyproof Sharing of Submodular Costs: budget balance versus efficiency
, 1999
"... A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served ..."
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Cited by 201 (19 self)
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A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and viceversa. We characterize the rich family of budget balanced and group strategyproof mechanisms; they correspond to the family of cost sharing formulae where an agent's cost share does not decrease when the set of users expand. The mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance  the more common route in the literature  we find that there is a single ClarkeGroves mech...
The Complexity of Pure Nash Equilibria
, 2004
"... We investigate from the computational viewpoint multiplayer games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLScomplete in general. ..."
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Cited by 169 (6 self)
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We investigate from the computational viewpoint multiplayer games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLScomplete in general. We discuss implications to nonatomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 152 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Adaptive Channel Allocation Spectrum Etiquette for Cognitive Radio Networks
 In Proc. of IEEE DySPAN
, 2005
"... In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish users and cooperative users, respectively. Bas ..."
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Cited by 141 (2 self)
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In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish users and cooperative users, respectively. Based on the utility definition for cooperative users, we show that the channel allocation problem can be formulated as a potential game, and thus converges to a deterministic channel allocation Nash equilibrium point. Alternatively, a noregret learning implementation is proposed for both scenarios and it is shown to have similar performance with the potential game when cooperation is enforced, but with a higher variability across users. The noregret learning formulation is particularly useful to accommodate selfish users. Noncooperative learning games have the advantage of a very low overhead for information exchange in the network. We show that cooperation based spectrum sharing etiquette improves the overall network performance at the expense of an increased overhead required for information exchange.
An introduction to collective intelligence
 Handbook of Agent technology. AAAI
, 1999
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Equilibrium Selection in Global Games with Strategic Complementarities
 Journal of Economic Theory
, 2003
"... We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and v ..."
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Cited by 136 (18 self)
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We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (1993) for two player, two action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noiseindependent selection.