Simple strategies for large zero-sum games with applications to complexity theory
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
A stronger bound on Braess's Paradox
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Bottleneck links, variable demand, and the tragedy of the commons
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the severity of Braess's paradox: designing networks for selfish users is hard
Journal of Computer and System Sciences - Special issue on FOCS 2001
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Atomic routing games on maximum congestion
Theoretical Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The hardness of selective network design for bottleneck routing games
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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
Braess's paradox, fibonacci numbers, and exponential inapproximability
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The hardness of network design for unsplittable flow with selfish users
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Bottleneck Routing Games in Communication Networks
IEEE Journal on Selected Areas in Communications
| Hi-index | 5.23 |
In routing games, the selfish behavior of the players may lead to a degradation of the network performance at equilibrium. In more than a few cases however, the equilibrium performance can be significantly improved if we remove some edges from the network. This counterintuitive fact, widely known as Braess@?s paradox, gives rise to the (selfish) network design problem, where we seek to recognize routing games suffering from the paradox, and to improve their equilibrium performance by edge removal. In this work, we investigate the computational complexity and the approximability of the network design problem for non-atomic bottleneck routing games, where the individual cost of each player is the bottleneck cost of her path, and the social cost is the bottleneck cost of the network, i.e. the maximum latency of a used edge. We first show that bottleneck routing games do not suffer from Braess@?s paradox either if the network is series-parallel, or if we consider only subpath-optimal Nash flows. On the negative side, we prove that even for games with strictly increasing linear latencies, it is NP-hard not only to recognize instances suffering from the paradox, but also to distinguish between instances for which the Price of Anarchy (PoA) can decrease to 1 and instances for which the PoA cannot be improved by edge removal, even if their PoA is as large as @W(n^0^.^1^2^1). This implies that the network design problem for linear bottleneck routing games is NP-hard to approximate within a factor of O(n^0^.^1^2^1^-^@e), for any constant @e0. The proof is based on a recursive construction of hard instances that carefully exploits the properties of bottleneck routing games, and may be of independent interest. On the positive side, we present an algorithm for finding a subnetwork that is almost optimal with respect to the bottleneck cost of its worst Nash flow, when the worst Nash flow in the best subnetwork routes a non-negligible amount of flow on all used edges. We show that the running time is essentially determined by the total number of paths in the network, and is quasipolynomial when the number of paths is quasipolynomial.