Stabilization of the minimum latency flow in Braess graphs by state-dependent tax

  • Authors:

  • Takurou Misaka;Takafumi Kanazawa;Toshimitsu Ushio;Yasuhiko Fukumoto

  • Affiliations:

  • Osaka University, Toyonaka, Osaka, Japan;Osaka University, Toyonaka, Osaka, Japan;Osaka University, Toyonaka, Osaka, Japan;Osaka University, Toyonaka, Osaka, Japan

  • Venue:
  • Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Sytems
  • Year:
  • 2008

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Abstract

A selfish routing game is a simple model of selfish behaviors in networks. Braess's paradox is a well-known example of inefficiencies existing in the selfish routing games and it is an important problem to reduce such inefficiencies. To resolve such a problem, a notion of a marginal cost tax has been proposed. Although the marginal cost tax makes the minimum latency flow a Nash equilibrium, it also imposes an additional latency on the minimum latency flow. Thus, we apply replicator dynamics with a subsidy and a capitation tax to Braess graphs and extend the capitation tax to a state-dependent one. Using two simplest Braess graphs B1 and B2, we show that the minimum latency flow of the Braess graphs can be stabilized by our proposed state-dependent tax.