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13
Social context games
 In WINE08
, 2008
"... Abstract. We introduce the study of social context games. A social context game is defined by an underlying game in strategic form, and a social context consisting of an undirected graph of neighborhood among players and aggregation functions. The players and strategies in a social context game are ..."
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Abstract. We introduce the study of social context games. A social context game is defined by an underlying game in strategic form, and a social context consisting of an undirected graph of neighborhood among players and aggregation functions. The players and strategies in a social context game are as in the underlying game, while the players ’ utilities in a social context game are computed from their payoffs in the underlying game based on the graph of neighborhood and the aggregation functions. Examples of social context games are ranking games and coalitional congestion games. A significant challenge is the study of how various social contexts affect various properties of the game. In this paper we consider resource selection games as the underlying games, and four basic social contexts. An important property of resource selection games is the existence of pure strategy equilibrium. We study the existence of pure strategy Nash equilibrium in the corresponding social context games. We also show that the social context games possessing pure strategy Nash equilibria are not potential games, and therefore are distinguished from congestion games. 1
Strong Price of Anarchy for Machine Load Balancing
"... Abstract. As defined by Aumann in 1959, a strong equilibrium is a Nash equilibrium that is resilient to deviations by coalitions. We give tight bounds on the strong price of anarchy for load balancing on related machines. We also give tight bounds for kstrong equilibria, where the size of a deviati ..."
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Cited by 9 (0 self)
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Abstract. As defined by Aumann in 1959, a strong equilibrium is a Nash equilibrium that is resilient to deviations by coalitions. We give tight bounds on the strong price of anarchy for load balancing on related machines. We also give tight bounds for kstrong equilibria, where the size of a deviating coalition is at most k.
Weighted congestion games: Price of anarchy, universal worstcase examples, and tightness
 In Proceedings of the 18th Annual European Symposium on Algorithms (ESA
, 2010
"... Abstract. We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (co ..."
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Cited by 8 (4 self)
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Abstract. We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost functionindependent) worstcase examples. One noteworthy byproduct of our proofs is the fact that weighted congestion games are “tight”, which implies that the worstcase price of anarchy with respect to pure Nash, mixed Nash, correlated, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worstcase POA, at least for polynomial cost functions. We also prove a new result about unweighted congestion games: the worstcase price of anarchy in symmetric games is, as the number of players goes to infinity, as large as in their more general asymmetric counterparts. 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 5 (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
An algorithmic game theory primer
, 2008
"... We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1 ..."
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We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1
How to tax and route selfish unsplittable traffic
 Proceedings of SPAA
, 2004
"... We consider general resource assignment games involving selfish users/agents in which users compete for resources and try to be assigned to resources which maximize their own benefits (e.g., try to route their traffic through links which minimize the latency of their own traffic). We propose and stu ..."
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Cited by 4 (1 self)
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We consider general resource assignment games involving selfish users/agents in which users compete for resources and try to be assigned to resources which maximize their own benefits (e.g., try to route their traffic through links which minimize the latency of their own traffic). We propose and study a mechanism design approach in which an allocation mechanism assigns users to resources and charges the users for using the resources so to induce each user to truthfully report a private piece of information he/she holds (e.g., how much traffic he/she needs to transmit). This information is crucial for computing optimal (or close to the optimal) allocations and an agent could misreport his/her information so to induce the underlying allocation algorithm to output a solution which he/she likes more (e.g., which assigns better resources to him/her). For our resource allocation problems, we give an algorithmic characterization of the solutions for which truthtelling is a Nash equilibrium. A natural application of these results is to a scheduling/routing problem which is the mechanism design “counterpart ” of the selfish routing game of Koutsoupias and Papadimitriou [1999]: Each selfish user wants to route a piece of
Stability and Convergence in Selfish Scheduling with Altruistic Agents
, 2009
"... In this paper we consider altruism, a phenomenon widely observed in nature and practical applications, in the prominent model of selfish load balancing with coordination mechanisms. Our model of altruistic behavior follows recent work by assuming that agent incentives are a tradeoff between selfish ..."
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Cited by 2 (1 self)
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In this paper we consider altruism, a phenomenon widely observed in nature and practical applications, in the prominent model of selfish load balancing with coordination mechanisms. Our model of altruistic behavior follows recent work by assuming that agent incentives are a tradeoff between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our results show that even in very simple cases a variety of standard coordination mechanisms are not robust against altruistic behavior, as pure Nash equilibria are absent or better response dynamics cycle. In contrast, we show that a recently introduced TimeSharing policy yields a potential game even for partially altruistic agents. In addition, for this policy a Nash equilibrium can be computed in polynomial time. In this way our work provides new insights on the robustness of coordination mechanisms. On a more fundamental level, our results highlight the limitations of stability and convergence when altruistic agents are introduced into games with weighted and lexicographical potential functions.
Selfish bin packing
 In ESA ’08: Proceedings of the sixteenth annual European Symposium on Algorithms
, 2008
"... Abstract. Following recent interest in the study of computer science problems in a game theoretic setting, we consider the well known bin packing problem where the items are controlled by selfish agents. Each agent is charged with a cost according to the fraction of the used bin space its item requi ..."
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Abstract. Following recent interest in the study of computer science problems in a game theoretic setting, we consider the well known bin packing problem where the items are controlled by selfish agents. Each agent is charged with a cost according to the fraction of the used bin space its item requires. That is, the cost of the bin is split among the agents, proportionally to their sizes. Thus, the selfish agents prefer their items to be packed in a bin that is as full as possible. The social goal is to minimize the number of the bins used. The social cost in this case is therefore the number of bins used in the packing. A pure Nash equilibrium is a packing where no agent can obtain a smaller cost by unilaterally moving his item to a different bin, while other items remain in their original positions. A Strong Nash equilibrium is a packing where there exists no subset of agents, all agents in which can profit from jointly moving their items to different bins. We say that all agents in a subset profit from moving their items to different bins if all of them have a strictly smaller cost as a result of moving, while the other items remain in their positions. We measure the quality of the equilibria using the standard measures PoA and PoS that are defined as the worst case worst/best asymptotic ratio between the social cost of a (pure) Nash equilibrium and the cost of an optimal packing, respectively. We also consider the recently introduced measures SPoA and SPoS, that are defined similarly to the PoA and the PoS, but consider only Strong Nash equilibria. We give nearly tight lower and upper bounds of 1.6416 and 1.6428, respectively, on the PoA of the bin packing game, improving upon previous result by Bilò, and establish the fact that P oS = 1. We show that the bin packing game admits a Strong Nash equilibrium, and that SPoA=SPoS. We prove that this value is equal to the approximation ratio of a natural greedy algorithm for bin packing. 1
Considerate Equilibrium
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We study the existence and computational complexity of coalitional stability concepts based on social networks. Our concepts represent a natural and rich combinatorial generalization of a recent notion termed partition equilibrium [5]. We assume that players in a strategic game are embedded in a soc ..."
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Cited by 1 (1 self)
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We study the existence and computational complexity of coalitional stability concepts based on social networks. Our concepts represent a natural and rich combinatorial generalization of a recent notion termed partition equilibrium [5]. We assume that players in a strategic game are embedded in a social (or, communication) network, and there are coordination constraints defining the set of coalitions that can jointly deviate in the game. A main feature of our approach is that players act in a “considerate” fashion to ignore potentially profitable (group) deviations if the change in their strategy may cause a decrease of utility to their neighbors in the network. We explore the properties of such considerate equilibria in application to the celebrated class of resource selection games (RSGs). Our main result proves existence of a superstrong considerate equilibrium in all symmetric RSGs with strictly increasing delays, for any social network among the players and feasible coalitions represented by the set of cliques. The existence proof is constructive and yields an efficient algorithm. In fact, the computed considerate equilibrium is a Nash equilibrium for a standard RSG, thus showing that there exists a state that is stable against selfish and considerate behavior simultaneously. Furthermore, we provide results on convergence of considerate dynamics.
MULTIPROCESSOR SCHEDULING is PLScomplete ∗
"... We consider two natural models of local improvement. We show that the MULTIPROCESSOR SCHEDULING problem, i.e., the problem of scheduling weighted jobs on identical machines with the objective to minimize the makespan, is PLScomplete for a sufficiently large neighborhood. In the first model, in an i ..."
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We consider two natural models of local improvement. We show that the MULTIPROCESSOR SCHEDULING problem, i.e., the problem of scheduling weighted jobs on identical machines with the objective to minimize the makespan, is PLScomplete for a sufficiently large neighborhood. In the first model, in an improvement step, either the makespan decreases or the makespan remains unchanged and the number of makespan machines decreases. In the second model, we consider the selfish version of the problem, where the jobs are viewed as selfish agents. The cost of an agent is the load of the machine to which it is assigned. Agents may form arbitrary, nonfixed coalitions. The cost of a coalition is defined to be the maximum cost of its members. In an improvement step, the cost of the coalition of reallocating agents decreases. Both these problems are PLScomplete for local improvement algorithms with steps which include reallocating up to 33 jobs/agents. We show these results by reduction from the MAXCONSTRAINTASSIGNMENT problem (p,q,r)MCA, which is an extension of weighted, generalized MAXSAT to higher valued variables. Here, p is the maximum number of variables occurring in a constraint, q is the maximum number of appearances of a variable, and r is the valuedness of the variables. In detail, we use a reduction from (2, 3, r)MCAbipartite, which is the restriction of (2,3,r)MCA to instances I, where the graph defined by I is bipartite, and we use some local version of the wellknown weighted 3DIMENSIONALMATCHING problem as an intermediate problem in our reduction. In contrast to our results, for k = 1 and k ∈ N, the solution computed by Graham’s LPTalgorithm is locally op