The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
An engineering approach to computer networking: ATM networks, the Internet, and the telephone network
Journal of the ACM (JACM)
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On selfish routing in internet-like environments
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Designing Networks for Selfish Users is Hard
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Efficiency Loss in a Network Resource Allocation Game
Mathematics of Operations Research
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the inefficiency of equilibria in congestion games
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands
Operations Research Letters
Characterizing the Existence of Potential Functions in Weighted Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Computing pure Nash and strong equilibria in bottleneck congestion games
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
A competitive strategy for routing flow over time
ACM SIGecom Exchanges
Congestion games with variable demands
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
Wardrop equilibria and price of stability for bottleneck games with splittable traffic
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Edge pricing of multicommodity networks for selfish users with elastic demands
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
A Stackelberg strategy for routing flow over time
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the hardness of network design for bottleneck routing games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
On the hardness of network design for bottleneck routing games
Theoretical Computer Science
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The price of anarchy, a measure of the inefficiency of selfish behavior, has been successfully analyzed in a diverse array of models over the past five years. The overwhelming majority of this work has studied optimization problems that sought an optimal way to allocate a fixed demand to resources whose performance degrades with increasing congestion. While fundamental, such problems overlook a crucial feature of many applications: the intrinsic coupling of the quality or cost of a resource and the demand for that resource. This coupling motivates allowing demand to vary with congestion, which in turn can lead to "the tragedy of the commons"---severe inefficiency caused by the overconsumption of a shared resource.Allowing the demand for resources to vary with their congestion illuminates a second issue with existing studies of the price of anarchy: the standard additive method of aggregating the costs of different resources in a player's strategy is inappropriate for some important applications, including many of those with variable demand. For example, in networking applications a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. This disconnect motivates consideration of nonlinear cost aggregation functions, such as the lp norms.In this paper, we initiate the study of the price of anarchy with variable demand and with broad classes of nonlinear aggregation functions. We focus on selfish routing in single- and multicommodity networks, and on the lp norms for 1 ≤ p ≤ ∞; our main results are as follows.• For a natural "prize-collecting" objective function, the price of anarchy in multicommodity networks with variable demand is no larger than that in fixed-demand networks. Thus the inefficiency arising from the tragedy of the commons is no more severe than that from routing inefficiencies.• Using the lp norm with 1 p l∞ norms as a cost aggregation function can dramatically increase the price of anarchy, even in single-commodity networks. If attention is restricted to equilibria with additional structure, however---structure that is ensured by distributed shortest-path routing protocols---then using the l∞ norm does not increase the price of anarchy relative to additive aggregation.