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38
Distributed selfish load balancing
, 2006
"... Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A gametheoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent”, and require each agent to select a resource, with the cost of a resource being the number of ..."
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Cited by 29 (1 self)
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Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A gametheoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent”, and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced. Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For m ≫ n, the system becomes approximately balanced (an ǫNash equilibrium) in expected time O(log log m). We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time O(log log m + n 4). We also give a lower bound of Ω(max{loglog m, n}) for the convergence time.
Pure Nash equilibria in playerspecific and weighted congestion games
 In Proc. of the 2nd Int. Workshop on Internet and Network Economics (WINE
, 2006
"... Additionally, our analysis of playerspecific matroid congestion games yields a polynomial time algorithm for computing pure equilibria. We also address questions related to the convergence time of such games. For playerspecific matroid congestion games, in which the best response dynamics may cycl ..."
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Cited by 19 (10 self)
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Additionally, our analysis of playerspecific matroid congestion games yields a polynomial time algorithm for computing pure equilibria. We also address questions related to the convergence time of such games. For playerspecific matroid congestion games, in which the best response dynamics may cycle, we show that from every state there exists a short sequences of better responses to an equilibrium. For weighted matroid congestion games, we present a superpolynomial lower bound on the convergence time of the best response dynamics showing that players do not even converge in pseudopolynomial time.
Congestion games: Optimization in competition
 In Proceedings of the 2nd Algorithms and Complexity in Durham Workshop
, 2006
"... abstract. In a congestion game, several players simultaneously aim at allocating sets of resources, e.g., each player aims at allocating a shortest path between a source/destination pair in a given network or, to give another example, each player aims at allocating a minimum weight spanning tree in ..."
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Cited by 13 (0 self)
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abstract. In a congestion game, several players simultaneously aim at allocating sets of resources, e.g., each player aims at allocating a shortest path between a source/destination pair in a given network or, to give another example, each player aims at allocating a minimum weight spanning tree in a given graph. The cost (length, delay, weight) of a resource (edge) is a function of the congestion, i.e., the number of players allocating the resource. In this paper, we survey recent results about the complexity of computing Nash equilibria for congestion games and the convergence time towards Nash equilibria. 1
Efficient coordination mechanisms for unrelated machine scheduling
 In: Proc. AMCSIAM SODA
, 2009
"... We present three new coordination mechanisms for scheduling n selfish jobs on m unrelated machines. A coordination mechanism aims to mitigate the impact of selfishness of jobs on the efficiency of schedules by defining a local scheduling policy on each machine. The scheduling policies induce a game ..."
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Cited by 11 (0 self)
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We present three new coordination mechanisms for scheduling n selfish jobs on m unrelated machines. A coordination mechanism aims to mitigate the impact of selfishness of jobs on the efficiency of schedules by defining a local scheduling policy on each machine. The scheduling policies induce a game among the jobs and each job prefers to be scheduled on a machine so that its completion time is minimum given the assignments of the other jobs. We consider the maximum completion time among all jobs as the measure of the efficiency of schedules. The approximation ratio of a coordination mechanism quantifies the efficiency of pure Nash equilibria (price of anarchy) of the induced game. Our mechanisms are deterministic, local, and preemptive in the sense that the scheduling policy does not necessarily process
Circumventing the Price of Anarchy: Leading Dynamics to Good Behavior
"... Abstract: Many natural games can have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. Yet, nearly all work to date on dynamics shows only convergence to some equilibrium, especially within a polynomial number of steps. In this work we study ..."
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Cited by 10 (4 self)
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Abstract: Many natural games can have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. Yet, nearly all work to date on dynamics shows only convergence to some equilibrium, especially within a polynomial number of steps. In this work we study how agents with some knowledge of the game might be able to quickly (within a polynomial number of steps) find their way to states of quality close to the best equilibrium. We consider two natural learning models in which players choose between greedy behavior and following a proposed good but untrusted strategy and analyze two important classes of games in this context, fair costsharing and consensus games. Both games have extremely high Price of Anarchy and yet we show that behavior in these models can efficiently reach lowcost states. Keywords: Dynamics in Games, Price of Anarchy, Price of Stability, Costsharing games, Consensus games, Learning from untrusted experts
Congestion games with playerspecific constants
 In Proceedings of the 32nd International Symposium on Mathematical Foundations of Computer Science
, 2007
"... Abstract. We consider a special case of weighted congestion games with playerspecific latency functions where each player uses for each particular resource a fixed (nondecreasing) delay function together with a playerspecific constant. For each particular resource, the resourcespecific delay fun ..."
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Cited by 10 (3 self)
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Abstract. We consider a special case of weighted congestion games with playerspecific latency functions where each player uses for each particular resource a fixed (nondecreasing) delay function together with a playerspecific constant. For each particular resource, the resourcespecific delay function and the playerspecific constant (for that resource) are composed by means of a group operation (such as addition or multiplication) into a playerspecific latency function. We assume that the underlying group is a totally ordered abelian group. In this way, we obtain the class of (weighted) congestion games with playerspecific constants; we observe that this class is contained in the new intuitive class of dominance (weighted) congestion games. Wefocusonpure Nash equilibria for congestion games with playerspecific constants; for these equilibria, we study questions of existence, computational complexity and convergence via improvement or bestreply steps of players. Our findings are as follows: – Games on parallel links: Every unweighted congestion game has an ordinal potential; hence,ithastheFinite Improvement Property and a pure Nash equilibrium. There is a weighted congestion game with 3 players on 3 parallel links that does not have
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 9 (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
Computing equilibria: A computational complexity perspective
, 2009
"... Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications ..."
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Cited by 7 (2 self)
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Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications for computation, games, and behavior. We assume
On the complexity of pure Nash equilibria in playerspecific network congestion games
 In WINE ’07
"... Abstract. Network congestion games with playerspecific delay functions do not necessarily possess pure Nash equilibria. We therefore address the computational complexity of the corresponding decision problem, and show that it is NPcomplete to decide whether such games possess pure Nash equilibria. ..."
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Cited by 6 (3 self)
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Abstract. Network congestion games with playerspecific delay functions do not necessarily possess pure Nash equilibria. We therefore address the computational complexity of the corresponding decision problem, and show that it is NPcomplete to decide whether such games possess pure Nash equilibria. This negative result still holds in the case of games with two players only. In contrast, we show that one can decide in polynomial time whether an equilibrium exists if the number of resources is constant. In addition, we introduce a family of playerspecific network congestion games which are guaranteed to possess equilibria. In these games players have identical delay functions, however, each player may only use a certain subset of the edges. For this class of games we prove that finding a pure Nash equilibrium is PLScomplete even in the case of three players. Again, in the case of a constant number of edges an equilibrium can be computed in polynomial time. We conclude that the number of resources has a bigger impact on the computation complexity of certain problems related to network congestion games than the number of players. 1