The design and analysis of algorithms
The design and analysis of algorithms
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Difference Between One and Many (Preliminary Version)
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Computing Nash equilibria for scheduling on restricted parallel links
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
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Structure and complexity of extreme Nash equilibria
Theoretical Computer Science - Game theory meets theoretical computer science
Tradeoffs in worst-case equilibria
Theoretical Computer Science - Approximation and online algorithms
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Selfish Load Balancing and Atomic Congestion Games
Algorithmica
On the structure and complexity of worst-case equilibria
Theoretical Computer Science
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Algorithmica
Selfish Routing with Incomplete Information
Theory of Computing Systems
A new model for selfish routing
Theoretical Computer Science
Mediated Equilibria in Load-Balancing Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Tradeoffs and Average-Case Equilibria in Selfish Routing
ACM Transactions on Computation Theory (TOCT)
Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
Symmetry in network congestion games: pure equilibria and anarchy cost
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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
Nash equilibrium for collective strategic reasoning
Expert Systems with Applications: An International Journal
Learning equilibria of games via payoff queries
Proceedings of the fourteenth ACM conference on Electronic commerce
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In a discrete routing game, each of n selfish users employs a mixed strategy to ship her (unsplittable) traffic over m parallel links. The (expected) latency on a link is determined by an arbitrary non-decreasing, non-constant and convex latency function @f. In a Nash equilibrium, each user alone is minimizing her (Expected) Individual Cost, which is the (expected) latency on the link she chooses. To evaluate Nash equilibria, we formulate Social Cost as the sum of the users' (Expected) Individual Costs. The Price of Anarchy is the worst-case ratio of Social Cost for a Nash equilibrium over the least possible Social Cost. A Nash equilibrium is pure if each user deterministically chooses a single link; a Nash equilibrium is fully mixed if each user chooses each link with non-zero probability. We obtain: For the case of identical users, the Social Cost of any Nash equilibrium is no more than the Social Cost of the fully mixed Nash equilibrium, which may exist only uniquely. Moreover, instances admitting a fully mixed Nash equilibrium enjoy an efficient characterization. For the case of identical users, we derive two upper bounds on the Price of Anarchy: For the case of identical links with a monomial latency function @f(x)=x^d, the Price of Anarchy is the Bell number of orderd+1. For pure Nash equilibria, a generic upper bound from the Wardrop model can be transfered to discrete routing games. For polynomial latency functions with non-negative coefficients and degree d, this yields an upper bound of d+1. For the case of identical users, a pure Nash equilibrium (and thereby an optimum pure assignment) can be computed in time O(mlogmlogn). For the general case, computing the best or the worst pure Nash equilibrium is NP-complete, even for identical links with an identity latency function.