Price of anarchy is maximized at the percolation threshold
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. Further, for large networks the value of the POA appears to saturate at its theoretical maximum value.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 1395037
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 91, Issue 5; ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
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