Stackelberg Routing in Arbitrary Networks
- 1 May 2010
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 35 (2), 330-346
- https://doi.org/10.1287/moor.1100.0442
Abstract
We investigate the impact of Stackelberg routing to reduce the price of anarchy in network routing games. In this setting, an α fraction of the entire demand is first routed centrally according to a predefined Stackelberg strategy and the remaining demand is then routed selfishly by (nonatomic) players. Although several advances have been made recently in proving that Stackelberg routing can, in fact, significantly reduce the price of anarchy for certain network topologies, the central question of whether this holds true in general is still open. We answer this question negatively by constructing a family of single-commodity instances such that every Stackelberg strategy induces a price of anarchy that grows linearly with the size of the network. Moreover, we prove upper bounds on the price of anarchy of the largest-latency-first (LLF) strategy that only depend on the size of the network. Besides other implications, this rules out the possibility to construct constant-size networks to prove an unbounded price of anarchy. In light of this negative result, we consider bicriteria bounds. We develop an efficiently computable Stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of 1 + √1−α. Finally, we analyze the effectiveness of an easy-to-implement Stackelberg strategy, called SCALE. We prove bounds for a general class of latency functions that includes polynomial latency functions as a special case. Our analysis is based on an approach that is simple yet powerful enough to obtain (almost) tight bounds for SCALE in general networks.Keywords
This publication has 30 references indexed in Scilit:
- Stackelberg Strategies for Selfish Routing in General Multicommodity NetworksAlgorithmica, 2007
- On the severity of Braess's Paradox: Designing networks for selfish users is hardJournal of Computer and System Sciences, 2006
- The multi-class, multi-criteria traffic network equilibrium and systems optimum problemTransportation Research Part B: Methodological, 2004
- How bad is selfish routing?Journal of the ACM, 2002
- Achieving network optima using Stackelberg routing strategiesIEEE/ACM Transactions on Networking, 1997
- An algorithm for the min concave cost flow problemEuropean Journal of Operational Research, 1980
- The existence, uniqueness and stability of traffic equilibriaTransportation Research Part B: Methodological, 1979
- The marginal cost taxation of a transportation networkTransportation Research Part B: Methodological, 1979
- ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH.Proceedings of the Institution of Civil Engineers, 1952
- Some Fallacies in the Interpretation of Social CostThe Quarterly Journal of Economics, 1924