Journal of the ACM (JACM)
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Selfish routing
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Prediction, Learning, and Games
Prediction, Learning, and Games
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Game Theory
Regret minimization and the price of total anarchy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Computing correlated equilibria in multi-player games
Journal of the ACM (JACM)
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Journal of Artificial Intelligence Research
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
Multiplicative updates outperform generic no-regret learning in congestion games: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Proceedings of the 10th ACM conference on Electronic commerce
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
Proceedings of the 28th ACM symposium on Principles of distributed computing
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Covering Games: Approximation through Non-cooperation
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Communications of the ACM
On the equilibria of alternating move games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Weighted congestion games: price of anarchy, universal worst-case examples, and tightness
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
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
WINE'10 Proceedings of the 6th international conference on Internet and network economics
GSP auctions with correlated types
Proceedings of the 12th ACM conference on Electronic commerce
On the efficiency of equilibria in generalized second price auctions
Proceedings of the 12th ACM conference on Electronic commerce
Mechanisms for (mis)allocating scientific credit
Proceedings of the forty-third annual ACM symposium on Theory of computing
Inner product spaces for MinSum coordination mechanisms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Restoring pure equilibria to weighted congestion games
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Efficiency of restricted tolls in non-atomic network routing games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
Local smoothness and the price of anarchy in atomic splittable congestion games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Welfare guarantees for combinatorial auctions with item bidding
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The robust price of anarchy of altruistic games
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Efficiency analysis of load balancing games with and without activation costs
Journal of Scheduling
Intrinsic robustness of the price of anarchy
Communications of the ACM
The price of anarchy in games of incomplete information
Proceedings of the 13th ACM Conference on Electronic Commerce
The price of anarchy for minsum related machine scheduling
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
The price of anarchy in games of incomplete information
ACM SIGecom Exchanges
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
Contention issues in congestion games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
A game-theoretic model of attention in social networks
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
Selfishness level of strategic games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
LP-Based covering games with low price of anarchy
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Smooth inequalities and equilibrium inefficiency in scheduling games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
Operations Research
Risk sensitivity of price of anarchy under uncertainty
Proceedings of the fourteenth ACM conference on Electronic commerce
Coevolutionary opinion formation games
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Composable and efficient mechanisms
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On a generalized Cournot oligopolistic competition game
Journal of Global Optimization
ACM Transactions on Economics and Computation
Coordination mechanisms from (almost) all scheduling policies
Proceedings of the 5th conference on Innovations in theoretical computer science
Mechanism design in large games: incentives and privacy
Proceedings of the 5th conference on Innovations in theoretical computer science
User satisfaction in competitive sponsored search
Proceedings of the 23rd international conference on World wide web
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The price of anarchy (POA) is a worst-case measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regret-minimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a "canonical sufficient condition" for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regret-minimizing players (or "price of total anarchy"). Smoothness arguments also have automatic implications for the inefficiency of approximate and Bayesian-Nash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomial-length best-response sequences. We also identify classes of games --- most notably, congestion games with cost functions restricted to an arbitrary fixed set --- that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worst-case upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with non-polynomial cost functions, and the first structural characterization of atomic congestion games that are universal worst-case examples for the POA.