How much can taxes help selfish routing?

  • Authors:

  • Richard Cole;Yevgeniy Dodis;Tim Roughgarden

  • Affiliations:

  • New York University, New York, NY;New York University, New York, NY;Cornell University, Ithaca, NY

  • Venue:
  • Proceedings of the 4th ACM conference on Electronic commerce
  • Year:
  • 2003

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Abstract

We study economic incentives for influencing selfish behavior in networks. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route traffic on minimum-latency paths. The quality of a routing of traffic is historically measured by the sum of all travel times, also called the total latency.It is well known that the outcome of selfish routing (a Nash equilibrium) does not minimize the total latency and can be improved upon with coordination, and that marginal cost pricing---charging each network user for the congestion effects caused by its presence---eliminates the inefficiency of selfish routing. However, the principle of marginal cost pricing assumes that (possibly very large) taxes cause no disutility to network users; this is appropriate only when collected taxes can be feasibly returned (directly or indirectly) to the users, for example via a lump-sum refund. If this assumption does not hold and we wish to minimize the total user disutility (latency plus taxes paid)---the total cost---how should we price the network edges? Intuition may suggest that taxes should never be able to improve the cost of a Nash equilibrium, but the famous Braess's Paradox shows this intuition to be incorrect.We consider strategies for pricing network edges to reduce the cost of a Nash equilibrium. Since levying a sufficiently large tax on an edge effectively removes it from the network, our study generalizes previous work on network design citend_hard. In this paper, we prove the following results.