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14
Beyond the Nash equilibrium barrier
 In Proc. of ICS
, 2011
"... Nash equilibrium analysis has become the de facto standard for judging the solution quality achieved in systems composed of selfish users. This mindset is so pervasive in computer science that even the few papers devoted to directly analyzing outcomes of dynamic processes in repeated games (e.g., be ..."
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Nash equilibrium analysis has become the de facto standard for judging the solution quality achieved in systems composed of selfish users. This mindset is so pervasive in computer science that even the few papers devoted to directly analyzing outcomes of dynamic processes in repeated games (e.g., bestresponse or noregret learning dynamics) have focused on showing that the performance of these dynamics is comparable to that of Nash equilibria. By assuming that equilibria are representative of the outcomes of selfish behavior, do we ever reach qualitatively wrong conclusions about those outcomes? In this paper, we argue that there exist games whose equilibria represent unnatural outcomes that are hard to coordinate on, and that the solution quality achieved by selfish users in such games is more accurately reflected in the disequilibrium represented by dynamics such as those produced by natural families of online learning algorithms. We substantiate this viewpoint by studying a game with a unique Nash equilibrium, but where natural learning dynamics exhibit nonconvergent cycling behavior rather than converging to this equilibrium. We show that the outcome of this learning process is optimal and has much better social welfare than the unique Nash equilibrium, dramatically illustrating that natural learning processes have the potential to significantly outperform equilibriumbased analysis.
The Curse of Simultaneity
"... Typical models of strategic interactions in computer science use simultaneous move games. However, in applications simultaneity is often hard or impossible to achieve. In this paper, we study the robustness of the Nash Equilibrium when the assumption of simultaneity is dropped. In particular we prop ..."
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Typical models of strategic interactions in computer science use simultaneous move games. However, in applications simultaneity is often hard or impossible to achieve. In this paper, we study the robustness of the Nash Equilibrium when the assumption of simultaneity is dropped. In particular we propose studying the sequential price of anarchy: the quality of outcomes of sequential versions of games whose simultaneous counterparts are prototypical in algorithmic game theory. We study different classes of games with high price of anarchy, and show that the subgame perfect equilibrium of their sequential version is a much more natural prediction, ruling out unreasonable equilibria, and leading to much better quality solutions. We consider three examples of such games: Cost Sharing
The Complexity of Equilibria in Cost Sharing Games
"... Abstract. We study Congestion Games with nonincreasing cost functions (Cost Sharing Games) from a complexity perspective and resolve their computational hardness, which has been an open question. Specifically we prove that when the cost functions have the form f(x) = cr/x (Fair Cost Allocation) th ..."
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Cited by 3 (1 self)
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Abstract. We study Congestion Games with nonincreasing cost functions (Cost Sharing Games) from a complexity perspective and resolve their computational hardness, which has been an open question. Specifically we prove that when the cost functions have the form f(x) = cr/x (Fair Cost Allocation) then it is PLScomplete to compute a Pure Nash Equilibrium even in the case where strategies of the players are paths on a directed network. For cost functions of the form f(x) = cr(x)/x, where cr(x) is a nondecreasing concave function we also prove PLScompleteness in undirected networks. Thus we extend the results of [7, 1] to the nonincreasing case. For the case of Matroid Cost Sharing Games, where tractability of Pure Nash Equilibria is known by [1] we give a greedy polynomial time algorithm that computes a Pure Nash Equilibrium with social cost at most the potential of the optimal strategy profile. Hence, for this class of games we give a polynomial time version of the Potential Method introduced in [2] for bounding the Price of Stability. Keywords: Cost Sharing, PLScompleteness, Price of Stability, Congestion Games 1
Near Optimality in Covering and Packing Games by Exposing Global
 Information, CoRR
"... Covering and packing problems can be modeled as games to encapsulate interesting social and engineering settings. These games have a high Price of Anarchy in their natural formulation. However, existing research applicable to specific instances of these games has only been able to prove fast converg ..."
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Covering and packing problems can be modeled as games to encapsulate interesting social and engineering settings. These games have a high Price of Anarchy in their natural formulation. However, existing research applicable to specific instances of these games has only been able to prove fast convergence to arbitrary equilibria. This paper studies general classes of covering and packing games with learning dynamics models that incorporate a central authority who broadcasts weak, socially beneficial signals to agents that otherwise only use local information in their decisionmaking. Rather than illustrating convergence to an arbitrary equilibrium that may have very high social cost, we show that these systems quickly achieve nearoptimal performance. In particular, we show that in the public service advertising model of [1], reaching a small constant fraction of the agents is enough to bring the system to a state within a logn factor of optimal in a broad class of set cover and set packing games or a constant factor of optimal in the special cases of vertex cover and maximum independent set, circumventing social inefficiency of bad local equilibria that could arise without a central authority. We extend these results to the learnthendecide model of [2], in which agents use any of a broad class of learning algorithms to decide in a given round whether to behave according to locally optimal behavior or the behavior prescribed by the broadcast signal. The new techniques we use for analyzing these games could be of broader interest for analyzing more general classic optimization problems in a distributed fashion. 1
The effects of diversity in aggregation games
 In Innovation in Computer Science
, 2011
"... Abstract: Aggregation of entities is a widely observed phenomenon in economics, sociology, biology and other fields. It is natural to ask how diverse and competitive entities can achieve high levels of aggregation. In order to answer this question we provide a gametheoretical model for aggregation. ..."
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Abstract: Aggregation of entities is a widely observed phenomenon in economics, sociology, biology and other fields. It is natural to ask how diverse and competitive entities can achieve high levels of aggregation. In order to answer this question we provide a gametheoretical model for aggregation. We consider natural classes of strategies for the individuals and show how this affects aggregation by studying the price of anarchy of the resulting game. Our analysis highlights the advantages of populations with diverse strategies (heterogeneous populations) over populations where all individuals share the same strategy (homogeneous populations). In particular, we prove that a simple heterogeneous population composed of leaders (individuals that tend to invest) and followers (individuals that look for shortterm rewards) achieves asymptotically lower price of anarchy compared to any homogeneous population, no matter how elaborate its strategy is. This sets forth the question of how diversity affects the problem solving abilities of populations in general. We hope that our work will lead to further research in games with diverse populations and in a better understanding of aggregation games.
Game Couplings: Learning Dynamics and Applications
"... Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is ..."
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Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is formally known about their properties and global dynamics. We investigate such distributed systems by introducing a novel gametheoretic construct, that we call gamecoupling. Game coupling intuitively allows us to stitch together the payoff structures of subgames. In order to study efficiency issues, we extend the price of anarchy approach (a major focus of gametheoretical multiagent systems [22]) to this setting, where we now care about the performance of each individual subsystem as well as the global performance. Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm. We prove matching welfare guarantees for both, both for individual subsystems as well as for the global system, using a generalization of the (λ, µ)smoothness framework [19]. In the second part of the paper, we work on understanding conditions that allow for wellstructured couplings. More generally, we examine when do game couplings preserve or enhance desirable properties of the original games, such as convergence of best response dynamics and low price of anarchy.
SANDIA REPORT Modeling AttackerDefender Interactions in Information Networks Modeling AttackerDefender Interactions in Information Networks
"... Abstract The simplest conceptual model of cybersecurity implicitly views attackers and defenders as acting in isolation from one another: an attacker seeks to penetrate or disrupt a system that has been protected to a given level, while a defender attempts to thwart particular attacks. Such a model ..."
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Abstract The simplest conceptual model of cybersecurity implicitly views attackers and defenders as acting in isolation from one another: an attacker seeks to penetrate or disrupt a system that has been protected to a given level, while a defender attempts to thwart particular attacks. Such a model also views all nonmalicious parties as having the same goal of preventing all attacks. But in fact, attackers and defenders are interacting parts of the same system, and different defenders have their own individual interests: defenders may be willing to accept some risk of successful attack if the cost of defense is too high. We have used game theory to develop models of how noncooperative but nonmalicious players in a network interact when there is a substantial cost associated with effective defensive measures. Although game theory has been applied in this area before, we have introduced some novel aspects of player behavior in our work, including • A model of how players attempt to avoid the costs of defense and force others to assume these costs • A model of how players interact when the cost of defending one node can be shared by other nodes • A model of the incentives for a defender to choose less expensive, but less effective, defensive actions. 3 Acknowledgment Thanks to Lyndon Pierson for suggesting this line of research, to Randall Laviolette and David Dumas for implementing a simulation of the iterated Aspnes Model, to Jared Saia for helpful discussions about game theory, and to Rolf Riesen for developing and maintaining the Latex sand report class. 4
1 Game Couplings: Learning Dynamics and Applications
"... Abstract — Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very ..."
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Abstract — Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is formally known about their properties and global dynamics. We investigate such distributed systems by introducing a novel gametheoretic construct, that we call gamecoupling. Game coupling intuitively allows us to stitch together the payoff structures of two or more games into a new game. In order to study efficiency issues, we extend the price of anarchy framework to this setting, where we now care about local and global performance. Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm. We prove matching welfare guarantees for both, both for individual subsystems as well as for the global system, using a generalization of the (λ, µ)smoothness framework [17]. In the second part of the paper, we establish conditions leading to advantageous couplings that preserve or enhance desirable properties of the original games, such as convergence of best response dynamics and low price of anarchy. I.
1.1 Examining what we mean by No Regret Algorithms in Games:
"... NOTE: The content of these notes has not been formally reviewed by the lecturer. It is recommended that they are read critically. ..."
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NOTE: The content of these notes has not been formally reviewed by the lecturer. It is recommended that they are read critically.