The complexity of pure Nash equilibria
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The Price of Routing Unsplittable Flow
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The price of anarchy of finite congestion games
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Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Selfish Routing with Incomplete Information
Theory of Computing Systems
Inapproximability of pure nash equilibria
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Fast convergence to nearly optimal solutions in potential games
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When Ignorance Helps: Graphical Multicast Cost Sharing Games
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On the impact of combinatorial structure on congestion games
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WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
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Selfish routing with oblivious users
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Exact price of anarchy for polynomial congestion games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On the price of anarchy and stability of correlated equilibria of linear congestion games,,
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Tight bounds for selfish and greedy load balancing
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Selfish load balancing under partial knowledge
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Social context congestion games
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
On bidimensional congestion games
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Social context congestion games
Theoretical Computer Science
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We consider weighted linear congestion games, and investigate how social ignorance, namely lack of information about the presence of some players, affects the inefficiency of pure Nash equilibria (PNE) and the convergence rate of the 驴-Nash dynamics. To this end, we adopt the model of graphical linear congestion games with weighted players, where the individual cost and the strategy selection of each player only depends on his neighboring players in the social graph. We show that such games admit a potential function, and thus a PNE. Our main result is that the impact of social ignorance on the Price of Anarchy (PoA) and the Price of Stability (PoS) is naturally quantified by the independence number 驴(G) of the social graph G. In particular, we show that the PoA grows roughly as 驴(G)(驴(G) + 2), which is essentially tight as long as 驴(G) does not exceed half the number of players, and that the PoS lies between 驴(G) and 2驴(G). Moreover, we show that the 驴-Nash dynamics reaches an 驴(G)(驴(G) + 2)-approximate configuration in polynomial time that does not directly depend on the social graph. For unweighted graphical linear games with symmetric strategies, we show that the 驴-Nash dynamics reaches an 驴-approximate PNE in polynomial time that exceeds the corresponding time for symmetric linear games by a factor at most as large as the number of players.