Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Tradeoffs in worst-case equilibria
Theoretical Computer Science - Approximation and online algorithms
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Utilitarian resource assignment
Journal of Discrete Algorithms
Selfish Load Balancing and Atomic Congestion Games
Algorithmica
The price of anarchy for polynomial social cost
Theoretical Computer Science
Selfish Routing with Incomplete Information
Theory of Computing Systems
Nash equilibria in discrete routing games with convex latency functions
Journal of Computer and System Sciences
The Influence of Link Restrictions on (Random) Selfish Routing
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
The Price of Stochastic Anarchy
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
The structure and complexity of Nash equilibria for a selfish routing game
Theoretical Computer Science
Theoretical Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Tradeoffs and average-case equilibria in selfish routing
ESA'07 Proceedings of the 15th 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
Smoothed performance guarantees for local search
ESA'11 Proceedings of the 19th European conference on Algorithms
Efficiency analysis of load balancing games with and without activation costs
Journal of Scheduling
Altruism in Atomic Congestion Games
ACM Transactions on Economics and Computation
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We study Nash equilibria in a selfish routing game on m parallel links with transmission speeds. Each player seeks to communicate a message by choosing one of the links, and each player desires to minimize his experienced transmission time (latency). For evaluating the social cost of Nash equilibria, we consider the price of anarchy, which is the largest ratio of the cost of any Nash equilibrium compared to the optimum solution. Similarly, we consider the price of stability, which is the smallest ratio. The main purpose of this article is to quantify the influence of three parameters upon the prices of the game: the total traffic in the network; restrictions of the players in terms of link choice; and fluctuations in message lengths. Our main interest is to bound the sum of all player latencies, which we refer to as collective latency. For this cost, the prices of anarchy and stability are Θ(n/t), where n is the number of players and t the sum of message lengths (total traffic); that is, Nash equilibria approximate the optimum solution up to a constant factor if the traffic is high. If each player is restricted to choose from a subset of links, these link restrictions can cause a degradation in performance of order Θ(\sqrt{m}). The prices of anarchy and stability increase to Θ(n\sqrt{m}/t). We capture fluctuations in message lengths through a stochastic model, in which we valuate Nash equilibria in terms of their expected price of anarchy. The expected price is Θ(n/\mathbb{E}[T]), where \mathbb{E}[T] is the expected traffic. The stochastic model resembles the deterministic one, even for the efficiency loss of order Θ(\sqrt{m}) for link restrictions. For the social cost function maximum latency, the (expected) price of anarchy is 1 + m2/t. In this case, Nash equilibria are almost optimal solutions for congested networks. Similar results hold when the cost function is a polynomial of the link loads.