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45
Intrinsic Robustness of the Price of Anarchy
 STOC'09
, 2009
"... The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium ..."
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Cited by 101 (12 self)
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The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regretminimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a “canonical sufficient condition ” for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regretminimizing players (or “price of total anarchy”). Smoothness arguments also have automatic implications for the inefficiency of approximate and BayesianNash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomiallength bestresponse sequences. We also identify classes of games — most notably, congestion games with cost functions restricted to an arbitrary fixed set — that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worstcase upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with nonpolynomial cost functions, and the first
Regret minimization and the price of total anarchy
, 2008
"... We propose weakening the assumption made when studying the price of anarchy: Rather than assume that selfinterested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret ..."
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Cited by 59 (10 self)
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We propose weakening the assumption made when studying the price of anarchy: Rather than assume that selfinterested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this “price of total anarchy” matches the Nash price of anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of anarchy and the recently introduced price of sinking [15], which require all players to behave in a prescribed manner, we show that the price of total anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total anarchy is an upper bound on the price of anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of anarchy in mixed strategies.
Altruism, selfishness, and spite in traffic routing
 In Proc. 9th Conf. Electronic Commerce (EC
, 2008
"... In this paper, we study the price of anarchy of traffic routing, under the assumption that users are partially altruistic or spiteful. We model such behavior by positing that the “cost ” perceived by a user is a linear combination of the actual latency of the route chosen (selfish component), and th ..."
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Cited by 24 (4 self)
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In this paper, we study the price of anarchy of traffic routing, under the assumption that users are partially altruistic or spiteful. We model such behavior by positing that the “cost ” perceived by a user is a linear combination of the actual latency of the route chosen (selfish component), and the increase in latency the user causes for others (altruistic component). We show that if all users have a coefficient of at least β> 0 for the altruistic component, then the price of anarchy is bounded by 1/β, for all network topologies, arbitrary commodities, and arbitrary semiconvex latency functions. We extend this result to give more precise bounds on the price of anarchy for specific classes of latency functions, even for β < 0 modeling spiteful behavior. In particular, we show that if all latency functions are linear, the price of anarchy is bounded by 4/(3 + 2β − β 2). We next study nonuniform altruism distributions, where different users may have different coefficients β. We prove that all such games, even with infinitely many types of players, have a Nash Equilibrium. We show that if the average of the coefficients for the altruistic components of all users is ¯ β, then the price of anarchy is bounded by 1 / ¯ β, for single commodity parallel link networks, and arbitrary convex latency functions. In particular, this result generalizes, albeit nonconstructively, the Stackelberg routing results of Roughgarden and of Swamy. More generally, we bound the price of anarchy based on the class of allowable latency functions, and as a corollary obtain tighter bounds for Stackelberg routing than a recent result of Swamy.
On the Windfall of Friendship: Inoculation Strategies on Social Networks
 EC'08
, 2008
"... This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environmen ..."
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Cited by 23 (2 self)
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This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environments. We analyze the corresponding equilibria and show that the computation of the worst and best Nash equilibrium is N Phard. Intriguingly, even though the windfall of friendship can never be negative, the social welfare does not increase monotonically with the extent to which players care for each other. While these phenomena are known on an anecdotal level, our framework allows us to quantify these effects analytically.
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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Cited by 18 (2 self)
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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.
The Price of Uncertainty
"... We study the degree to which small fluctuations in costs in wellstudied potential games can impact the result of natural bestresponse and improvedresponse dynamics. We call this the Price of Uncertainty and study it in a wide variety of potential games (including fair costsharing games, setcover ..."
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Cited by 14 (5 self)
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We study the degree to which small fluctuations in costs in wellstudied potential games can impact the result of natural bestresponse and improvedresponse dynamics. We call this the Price of Uncertainty and study it in a wide variety of potential games (including fair costsharing games, setcover games, routing games, and jobscheduling games), finding a number of surprising results. In particular, we show that in certain cases, even extremely small fluctuations can cause these dynamics to spin out of control and move to states of much higher social cost, whereas in other cases these dynamics are much more stable even to large degrees of fluctuation. We also consider the resilience of these dynamics to a small number of Byzantine players about which no assumptions are made. We show again a contrast between different games. In certain cases (e.g., fair costsharing, setcovering, jobscheduling) even a single Byzantine
The robust price of anarchy of altruistic games
 In Proc. 7th Workshop on Internet and Network Economics (WINE
, 2011
"... We study the inefficiency of equilibria for several classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i’s perceived cost is a convex combination of 1−αi times his direct cost and αi times the social cost. Tuning the parameters αi allows sm ..."
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Cited by 14 (3 self)
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We study the inefficiency of equilibria for several classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i’s perceived cost is a convex combination of 1−αi times his direct cost and αi times the social cost. Tuning the parameters αi allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study altruistic extensions of costsharing games, utility games, and linear congestion games. Our main contribution is an adaptation of Roughgarden’s smoothness notion to altruistic extensions of games. We show that this extension captures the essential properties to determine the robust price of anarchy of these games, and use it to derive mostly tight bounds. For congestion games and costsharing games, the worstcase robust price of anarchy increases with increasing altruism, while for utility games, it remains constant and is not affected by altruism. However, the increase in the price of anarchy is not a universal phenomenon: for symmetric singleton linear congestion games, the pure price of anarchy decreases both under increasing uniform altruism and as the fraction of entirely altruistic individuals increases.
Malicious Bayesian Congestion Games
 6th Workshop on Approximation and Online Algorithms (WAOA
, 2008
"... Abstract. In this paper, we introduce malicious Bayesian congestion games as an extension to congestion games where players might act in a malicious way. In such a game each player has two types. Either the player is a rational player seeking to minimize her own delay, or – with a certain probabilit ..."
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Cited by 12 (0 self)
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Abstract. In this paper, we introduce malicious Bayesian congestion games as an extension to congestion games where players might act in a malicious way. In such a game each player has two types. Either the player is a rational player seeking to minimize her own delay, or – with a certain probability – the player is malicious in which case her only goal is to disturb the other players as much as possible. We show that such games do in general not possess a Bayesian Nash equilibrium in pure strategies (i.e. a pure Bayesian Nash equilibrium). Moreover, given a game, we show that it is NPcomplete to decide whether it admits a pure Bayesian Nash equilibrium. This result even holds when resource latency functions are linear, each player is malicious with the same probability, and all strategy sets consist of singleton sets of resources. For a slightly more restricted class of malicious Bayesian congestion games, we provide easy checkable properties that are necessary and sufficient for the existence of a pure Bayesian Nash equilibrium. In the second part of the paper we study the impact of the malicious types on the overall performance of the system (i.e. the social cost). To measure this impact, we use the Price of Malice. We provide (tight) bounds on the Price of Malice for an interesting class of malicious Bayesian congestion games. Moreover, we show that for certain congestion games the advent of malicious types can also be beneficial to the system in the sense that the social cost of the worst case equilibrium decreases. We provide a tight bound on the maximum factor by which this happens. 1
A Survey of Interdependent Security Games
, 2012
"... Interdependence of information systems is a fundamental property that shapes the problems in information security. The risks faced by system operators and users is not only determined by their own security posture, but is heavily affected by the securityrelated decisions of other connected systems. ..."
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Cited by 9 (5 self)
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Interdependence of information systems is a fundamental property that shapes the problems in information security. The risks faced by system operators and users is not only determined by their own security posture, but is heavily affected by the securityrelated decisions of other connected systems. Therefore, defending networked systems relies on the correlated action of the system operators or users. In this survey, we summarize gametheoretic interdependence models, characterize the emerging security inefficiencies and present solution methods. Our goal is to distill the main insights from the stateoftheart and to identify the areas that need more attention from the research community. 1