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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 13 (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.
Nonclairvoyant scheduling games
 IN: PROC. 2ND INTL. SYMP. ALGORITHMIC GAME THEORY (SAGT
, 2009
"... In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their c ..."
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Cited by 11 (0 self)
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In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy – the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these socalled nonclairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules
Strong nash equilibria in games with the lexicographical improvement property
 Internet and Network Economics
, 2009
"... Abstract. We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Le ..."
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Cited by 11 (2 self)
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Abstract. We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Lexicographical Improvement Property (LIP) and show that it implies the existence of a generalized strong ordinal potential function. We use this characterization to derive existence, efficiency and fairness properties of strong Nash equilibria. We then study a class of games that generalizes congestion games with bottleneck objectives that we call bottleneck congestion games. We show that these games possess the LIP and thus the above mentioned properties. For bottleneck congestion games in networks, we identify cases in which the potential function associated with the LIP leads to polynomial time algorithms computing a strong Nash equilibrium. Finally, we investigate the LIP for infinite games. We show that the LIP does not imply the existence of a generalized strong ordinal potential, thus, the existence of SNE does not follow. Assuming that the function associated with the LIP is continuous, however, we prove existence of SNE. As a consequence, we prove that bottleneck congestion games with infinite strategy spaces and continuous cost functions possess a strong Nash equilibrium. 1
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
, 2012
"... We study the existence of pure Nash equilibria in weighted congestion games. Let C denote a set of cost functions. We say that C is consistent if every weighted congestion game with cost functions in C possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consist ..."
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Cited by 10 (2 self)
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We study the existence of pure Nash equilibria in weighted congestion games. Let C denote a set of cost functions. We say that C is consistent if every weighted congestion game with cost functions in C possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of continuous cost functions. We prove that a set C of continuous functions is consistent for twoplayer games if and only if C contains only monotonic functions and for all nonconstant functions c11 c2 ∈C, there are constants a1b ∈ such that c14x5 = ac24x5+ b for all x ∈≥0. For games with at least three players, we prove that C is consistent if and only if exactly one of the following cases holds: (a) C contains only affine functions; (b) C contains only exponential functions such that c4x5 = ac ex + bc for some ac1 bc1 ∈ , where ac and bc may depend on c, while must be equal for every c ∈ C. The latter characterization is even valid for threeplayer games. Finally, we derive several characterizations of consistency of cost functions for games with restricted strategy spaces, such as weighted network congestion games or weighted congestion games with singleton strategies.
Load balancing via random local search in closed and open systems
 In Proc. of SIGMETRICS
, 2010
"... In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load ..."
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In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., JointheShortestQueue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner. We first analyze the natural Random Local Search (RLS)
Distributed Algorithms for QoS Load Balancing ∗
"... We consider a dynamic load balancing scenario in which users allocate resources in a noncooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resources ..."
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Cited by 8 (2 self)
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We consider a dynamic load balancing scenario in which users allocate resources in a noncooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resources in a roundbased fashion. As opposed to various settings analyzed in the literature, we assume that users have quality of service (QoS) demands. A user has zero utility when falling short of a certain minimum performance threshold and having positive utility otherwise. Whereas various loadbalancing protocols have been proposed for the setting without quality of service requirements, we consider protocols that satisfy an additional locality constraint: The behavior of a user depends merely on the state of the resource it currently allocates. This property is particularly useful in scenarios where the state of other resources is not readily accessible. For instance, if resources represent channels in a mobile network, then accessing channel information may require timeintensive measurements. We consider several variants of the model, where the quality of service demands may depend on the user, the resource, or both. For all cases we present protocols for which the dynamics converge to a state in which all users are satisfied. More importantly, the time to reach such a state scales nicely. It is only logarithmic in the number of users, which makes our protocols applicable in largescale systems.
Balls into Bins via Local Search
, 2012
"... We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, wher ..."
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Cited by 4 (1 self)
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We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. In our main result, we prove thatthisprocessyieldsamaximumloadofonlyΘ(loglogn)onexpandergraphs. Inaddition, ( ( logn we show that for ddimensional grids the maximum load is Θ loglogn) 1 d+1. Finally, for almost regular graphs with minimum degree Ω(logn), we prove that the maximum load is constantandalsorevealafundamentaldifferencebetweenrandomandarbitrarytiebreaking rules. 1
Congestion Games with Capacitated Resources
"... We extend congestion games to the setting where every resource is endowed with a capacity which possibly limits its number of users. From the negative side, we show that a pure Nash equilibrium is not guaranteed to exist in any case and we prove that deciding whether a game possesses a pure Nash eq ..."
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Cited by 2 (1 self)
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We extend congestion games to the setting where every resource is endowed with a capacity which possibly limits its number of users. From the negative side, we show that a pure Nash equilibrium is not guaranteed to exist in any case and we prove that deciding whether a game possesses a pure Nash equilibrium is NPcomplete. Our positive results state that congestion games with capacities are potential games in the well studied singleton case. Polynomial algorithms that compute these equilibria are also provided.