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On the Value of Coordination in Network Design
"... We study network design games where n selfinterested agents have to form a network by purchasing links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge. It is well known that the price of anarchy o ..."
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We study network design games where n selfinterested agents have to form a network by purchasing links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge. It is well known that the price of anarchy of these games is as high as n. Therefore, recent research has focused on evaluating the price of stability, i.e. the cost of the best Nash equilibrium relative to the social optimum. In this paper we investigate to which extent coordination among agents can improve the quality of solutions. We resort to the concept of strong Nash equilibria, which were introduced by Aumann and are resilient to deviations by coalitions of agents. We analyze the price of anarchy of strong Nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs. These bounds are tight or nearly tight for many scenarios. It shows that using coordination, the price of anarchy drops from linear to logarithmic bounds. We complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria (without coordination) in undirected graphs. More specifically, we show a lower bound of Ω(log W / log log W) for weighted games, where W is the total weight of all the agents. This almost matches the known upper bound of O(log W). Our results imply that, for most settings, the worstcase performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination. These settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs.
Competitive Contagion in Networks
"... We develop a gametheoretic framework for the study of competition between firms who have budgets to “seed ” the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochasti ..."
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We develop a gametheoretic framework for the study of competition between firms who have budgets to “seed ” the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochastic diffusion process in the network. This framework yields a rich class of competitive strategies, which depend in subtle ways on the stochastic dynamics of adoption, the relative budgets of the players, and the underlying structure of the social network. We identify a general property of the adoption dynamics — namely, decreasing returns to local adoption — for which the inefficiency of resource use at equilibrium (the Price of Anarchy) is uniformly bounded above, across all networks. We also show that if this property is violated the Price of Anarchy can be unbounded, thus yielding sharp threshold behavior for a broad class of dynamics. We also introduce a new notion, the Budget Multiplier, that measures the extent that imbalances in player budgets can be amplified at equilibrium. We again identify a general property of the adoption dynamics — namely, proportional local adoption between competitors — for which the (pure strategy) Budget Multiplier is uniformly bounded above, across all networks. We show that a violation of this property can lead to unbounded Budget Multiplier, again yielding sharp threshold behavior for a broad class of dynamics.
Network formation games and the potential function method
 Algorithmic Game Theory, chapter 19
, 2007
"... Large computer networks such as the Internet are built, operated, and used by a large number of diverse and competitive entities. In light of these competing forces, it is surprising how efficient these networks are. An exciting challenge in the area of algorithmic game theory is to understand the s ..."
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Large computer networks such as the Internet are built, operated, and used by a large number of diverse and competitive entities. In light of these competing forces, it is surprising how efficient these networks are. An exciting challenge in the area of algorithmic game theory is to understand the success of these networks in game theoretic terms: what principles of interaction lead selfish participants to form such efficient networks? In this chapter we present a number of network formation games. We focus on simple games that have been analyzed in terms of the efficiency loss that results from selfishness. We also highlight a fundamental technique used in analyzing inefficiency in many games: the potential function method. The design and operation of many large computer networks, such as the Internet, are carried out by a large number of independent service providers (Autonomous Systems), all of whom seek to selfishly optimize the quality and cost of their own operation. Game theory provides a natural framework for modeling such selfish interests and
The Price of Anarchy in Games of Incomplete Information
 EC'12
, 2012
"... We define smooth games of incomplete information. We prove an “extension theorem” for such games: price of anarchy bounds for pure Nash equilibria for all induced fullinformation games extend automatically, without quantitative degradation, to all mixedstrategy BayesNash equilibria with respect t ..."
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We define smooth games of incomplete information. We prove an “extension theorem” for such games: price of anarchy bounds for pure Nash equilibria for all induced fullinformation games extend automatically, without quantitative degradation, to all mixedstrategy BayesNash equilibria with respect to a product prior distribution over players’ preferences. We also note that, for BayesNash equilibria in games with correlated player preferences, there is no general extension theorem for smooth games. We give several applications of our definition and extension theorem. First, we show that many games of incomplete information for which the price of anarchy has been studied are smooth in our sense. Thus our extension theorem unifies much of the known work on the price of anarchy in games of incomplete information. Second, we use our extension theorem to prove new bounds on the price of anarchy of BayesNash equilibria in congestion games with incomplete information.
Distributed Welfare Games
"... We consider a variation of the resource allocation problem. In the traditional problem, there is a global planner who would like to assign a set of players to a set of resources so as to maximize welfare. We consider the situation where the global planner does not have the authority to assign player ..."
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We consider a variation of the resource allocation problem. In the traditional problem, there is a global planner who would like to assign a set of players to a set of resources so as to maximize welfare. We consider the situation where the global planner does not have the authority to assign players to resources; rather, players are selfinterested. The question that emerges is how can the global planner entice the players to settle on a desirable allocation with respect to the global welfare? To study this question, we focus on a class of games that we refer to as distributed welfare games. Within this context, we investigate how the global planner should distribute the welfare to the players. We measure the efficacy of a distribution rule in two ways: (i) Does a pure Nash equilibrium exist? (ii) How does the welfare associated with a pure Nash equilibrium compare to the global welfare associated with the optimal allocation? In this paper we explore the applicability of cost sharing methodologies for distributing welfare in such resource allocation problems. We demonstrate that obtaining desirable distribution rules, such as distribution rules that are budget balanced and guarantee the existence of a pure Nash equilibrium, often comes at a significant informational and computational cost. In light of this, we derive a systematic procedure for designing desirable distribution rules with a minimal informational and computational cost for a special class of distributed welfare games. Furthermore, we derive a bound on the price of anarchy for distributed welfare games in a variety of settings. Lastly, we highlight the implications of these results using the problem of sensor coverage.
Extreme nash equilibria
 In Proc. of the 8th Italian Conference on Theoretical Computer Science, LNCS 2841
, 2003
"... Abstract. We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a ..."
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Abstract. We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel links, to control the routing of its own assigned traffic. InaNash equilibrium, each user routes its traffic on links that minimize its expected latency cost. Our structural results provide substantial evidence for the Fully Mixed Nash Equilibrium Conjecture, which states that the worst Nash equilibrium is the fully mixed Nash equilibrium, where each user chooses each link with positive probability. Specifically, we prove that the Fully Mixed Nash Equilibrium Conjecture is valid for pure Nash equilibria and that under a certain condition, the social cost of any Nash equilibrium is within a factor of 6 + ε, of that of the fully mixed Nash equilibrium, assuming that link capacities are identical.
Computer science and game theory: A brief survey
 Palgrave Dictionary of Economics
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Utilitybased Sensor Selection
, 2006
"... Sensor networks consist of many small sensing devices that monitor an environment and communicate using wireless links. The lifetime of these networks is severely curtailed by the limited battery power of the sensors. One line of research in sensor network lifetime management has examined sensor sel ..."
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Cited by 19 (1 self)
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Sensor networks consist of many small sensing devices that monitor an environment and communicate using wireless links. The lifetime of these networks is severely curtailed by the limited battery power of the sensors. One line of research in sensor network lifetime management has examined sensor selection techniques, in which applications judiciously choose which sensors ’ data should be retrieved and are worth the expended energy. In the past, many adhoc approaches for sensor selection have been proposed. In this paper, we argue that sensor selection should be based upon a tradeoff between applicationperceived benefit and energy consumption of the selected sensor set. We propose a framework wherein the application can specify the utility of measuring data (nearly) concurrently at each set of sensors. The goal is then to select a sequence of sets to measure whose total utility is maximized, while not exceeding the available energy.
On the value of correlation
 IN UAI05: PROCEEDINGS OF THE 21TH ANNUAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2005
"... Correlated equilibrium [1] generalizes Nash equilibrium to allow correlation devices. Aumann showed an example of a game, and of a correlated equilibrium in this game, in which the agents’ surplus (expected sum of payoffs) is greater than their surplus in all mixedstrategy equilibria. Following th ..."
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Correlated equilibrium [1] generalizes Nash equilibrium to allow correlation devices. Aumann showed an example of a game, and of a correlated equilibrium in this game, in which the agents’ surplus (expected sum of payoffs) is greater than their surplus in all mixedstrategy equilibria. Following the idea initiated by the price of anarchy literature [2, 3] this suggests the study of two major measures for the value of correlation in a game with nonnegative payoffs: 1. The ratio between the maximal surplus obtained in a correlated equilibrium to the maximal surplus obtained in a mixedstrategy equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the maximal surplus to the maximal surplus obtained in a correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation and enforcement values, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games [4], a class of games that received a lot of attention in the recent literature.
The Price of Malice in Linear Congestion Games
, 2008
"... We study the price of malice in linear congestion games using the technique of noregret analysis in the presence of Byzantine players. Our assumptions about the behavior both of rational players, and of malicious players are strictly weaker than have been previously used to study the price of malic ..."
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We study the price of malice in linear congestion games using the technique of noregret analysis in the presence of Byzantine players. Our assumptions about the behavior both of rational players, and of malicious players are strictly weaker than have been previously used to study the price of malice. Rather than assuming that rational players route their flow according to a Nash equilibrium, we assume only that the play so as to have no regret. Rather than assuming that malicious players myopically seek to maximize the social cost of the game, we study Byzantine players about whom we make no assumptions, who may be seeking to optimize any utility function, and who may engage in an arbitrary degree of counterspeculation. Because our assumptions are strictly weaker than in previous work, the bounds we prove on two measures of the price of malice hold also for the quantities studied by Babaioff et al. [2] and Moscibroda et al. [17] We prove tight bounds both for the special case of parallel link routing games, and for general congestion games.