The price of anarchy is maximized at the percolation threshold
arXiv:1404.2935 · doi:10.1103/PhysRevE.91.052126
Abstract
When many independent users try to route traffic through a network, the flow can easily become suboptimal as a consequence of congestion of the most efficient paths. The degree of this suboptimality is quantified by the so-called "price of anarchy" (POA), but so far there are no general rules for when to expect a large POA in a random network. Here I address this question by introducing a simple model of flow through a network with randomly-placed "congestible" and "incongestible" links. I show that the POA is maximized precisely when the fraction of congestible links matches the percolation threshold of the lattice. Both the POA and the total cost demonstrate critical scaling near the percolation threshold.
arXiv comment6+2 pages, 8+2 figures; additional figures and improved scaling analysis added
References in corpus (7)
- Epidemics and percolation in small-world networks
- Criticality and isostaticity in fiber networks
- The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control
- Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
- A Measure of data-collapse for scaling
- The price of anarchy in basketball
- Advection of passive particles over flow networks