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37
Tight bounds for selfish and greedy load balancing
 ICALP 2006. LNCS
, 2006
"... Abstract. We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it ..."
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Cited by 41 (5 self)
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Abstract. We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it selects to run its job to the server among its permissible servers having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness. We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy and price of stability of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions. 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 21 (1 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
Improved Equilibria via Public Service Advertising
"... Many natural games have both high and low cost Nash equilibria: their Price of Anarchy is high and yet their Price of Stability is low. In such cases, one could hope to move behavior from a high cost equilibrium to a low cost one by a “public service advertising campaign ” encouraging players to fol ..."
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Cited by 21 (7 self)
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Many natural games have both high and low cost Nash equilibria: their Price of Anarchy is high and yet their Price of Stability is low. In such cases, one could hope to move behavior from a high cost equilibrium to a low cost one by a “public service advertising campaign ” encouraging players to follow the lowcost equilibrium, and if every player follows the advice then we are done. However, the assumption that everyone follows instructions is unrealistic. A more natural assumption is that some players will follow them, while other players will not. In this paper we consider the question of to what extent can such an advertising campaign cause behavior to switch from a bad equilibrium to a good one even if only a fraction of people actually follow the given advice, and do so only temporarily. Unlike
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
Circumventing the Price of Anarchy: Leading Dynamics to Good Behavior
"... 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 age ..."
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Cited by 13 (6 self)
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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.
Approximating Pure Nash Equilibrium in Cut, Party Affiliation, and Satisfiability Games
"... Cut games and party affiliation games are wellknown classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLScom ..."
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Cited by 11 (1 self)
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Cut games and party affiliation games are wellknown classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLScomplete. We show that for any ɛ> 0, we design an algorithm to compute in polynomial time a (3 + ɛ)approximate pure Nash equilibrium for cut and party affiliation games. Prior to our work, only a trivial polynomial factor approximation was known for these games. Our approach extends beyond cut and party affiliation games to a more general class of satisfiability games. A key idea in our approach is a preprocessing phase that creates a partial order on the players. We then apply Nash dynamics to a sequence of restricted games derived from this partial order. We show that this process converges in polynomialtime to an approximate Nash equilibrium by strongly utilizing the properties of the partial order. This is in strong contrast to earlier results for some other classes of potential games that compute an approximate equilibrium by a direct application of Nash dynamics on the original game. In fact, we also show that such a technique cannot yield FPTAS for computing equilibria in cut and party affiliation games.
Flows and Decompositions of Games: Harmonic and Potential Games
"... In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze na ..."
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Cited by 11 (2 self)
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In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the wellknown potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the
On strong equilibria in the max cut game
 In: Proc. of WINE 2009, Springer LNCS
, 2009
"... Abstract. This paper deals with two games defined upon well known generalizations of max cut. We study the existence of a strong equilibrium which is a refinement of the Nash equilibrium. Bounds on the price of anarchy for Nash equilibria and strong equilibria are also given. In particular, we show ..."
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Cited by 9 (1 self)
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Abstract. This paper deals with two games defined upon well known generalizations of max cut. We study the existence of a strong equilibrium which is a refinement of the Nash equilibrium. Bounds on the price of anarchy for Nash equilibria and strong equilibria are also given. In particular, we show that the max cut game always admits a strong equilibrium and the strong price of anarchy is 2/3. 1
Atomic congestion games: fast, myopic and concurrent
"... We study here the effect of concurrent greedy moves of players in atomic congestion games where n selfish agents (players) wish to select a resource each (out of m resources) so that her selfish delay there is not much. Such games usually admit a global potential that decreases by sequential and se ..."
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Cited by 7 (0 self)
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We study here the effect of concurrent greedy moves of players in atomic congestion games where n selfish agents (players) wish to select a resource each (out of m resources) so that her selfish delay there is not much. Such games usually admit a global potential that decreases by sequential and selfishly improving moves. However, concurrent moves may not always lead to global convergence. On the other hand, concurrent play is desirable because it might essentially improve the system convergence time to some balanced state. The problem of “maintaining ” global progress while allowing concurrent play is exactly what is examined and answered here. We examine two orthogonal settings: (i) A game where the players decide their moves without global information, each acting “freely ” by sampling resources randomly and locally deciding to migrate (if the new resource is better) via a random experiment. Here, the resources can have quite arbitrary latency that is load dependent. (ii) An “organised” setting where the players are prepartitioned into selfish groups (coalitions) and where each coalition does an improving coalitional move. Here the concurrency is among the members of the coalition. In this second setting, the resources have latency functions that are only linearly dependent on the load, since this is the only case so far where a global potential exists. In both cases (i), (ii) we show that the system converges to an “approximate” equilibrium very fast (in