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According to Wardrop's first principle, agents in a congested network choose their
routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying
noncooperative game. A Nash equilibrium does not optimize any global criterion per
se, and so there is no apparent reason why it should be close to a solution of minimal
total travel time, i.e. the system optimum. In this paper, we offer extensions of recent
positive results on the efficiency of Nash equilibria in traffic networks. In contrast to
prior work, we present results for networks with capacities and for latency functions
that are nonconvex, nondifferentiable and even discontinuous. The inclusion of upper
bounds on arc flows has early been recognized as an important means to provide a
more accurate description of traffic flows. In this more general model, multiple Nash
equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient.
Nonetheless, our main result shows that the best equilibrium is as efficient as in the
model without capacities. Moreover, this holds true for broader classes of travel cost
functions than considered hithert |
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