The weighted majority algorithm
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Economics of location:: a selective survey
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Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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Proceedings of the twenty-second annual symposium on Principles of distributed computing
Adaptive routing with end-to-end feedback: distributed learning and geometric approaches
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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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Sink Equilibria and Convergence
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Anytime algorithms for multi-armed bandit problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Robbing the bandit: less regret in online geometric optimization against an adaptive adversary
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Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Selfish Load Balancing and Atomic Congestion Games
Algorithmica
Playing games with approximation algorithms
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Congestion games with malicious players
Proceedings of the 8th ACM conference on Electronic commerce
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'99 Proceedings of the 16th 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
Market sharing games applied to content distribution in ad hoc networks
IEEE Journal on Selected Areas in Communications
Fault tolerance in large games
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The Price of Stochastic Anarchy
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The Price of Malice in Linear Congestion Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Intrinsic robustness of the price of anarchy
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On the convergence of regret minimization dynamics in concave games
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Multiplicative updates outperform generic no-regret learning in congestion games: extended abstract
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Algorithmic Game Theory: A Snapshot
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Load balancing without regret in the bulletin board model
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Brief announcement: distributed algorithms for approximating wireless network capacity
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On the Inefficiency Ratio of Stable Equilibria in Congestion Games
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Online distributed sensor selection
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Distributed algorithms for approximating wireless network capacity
INFOCOM'10 Proceedings of the 29th conference on Information communications
From optimization to regret minimization and back again
SysML'08 Proceedings of the Third conference on Tackling computer systems problems with machine learning techniques
On learning algorithms for nash equilibria
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
The limits of smoothness: a primal-dual framework for price of anarchy bounds
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GSP auctions with correlated types
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Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
Local smoothness and the price of anarchy in atomic splittable congestion games
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Welfare guarantees for combinatorial auctions with item bidding
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Intrinsic robustness of the price of anarchy
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We propose weakening the assumption made when studying the price of anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total anarchy" matches the Nash price of anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of anarchy and the recently introduced price of sinking, which require all players to behave in a prescribed manner, we show that the price of total anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total anarchy is an upper bound on the price of anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of anarchy in mixed strategies.