Abstract | We investigate the existence of optimal tolls for atomic symmetric
network congestion games with unsplittable traffic and arbitrary non-negative and
non-decreasing latency functions.We focus on pure Nash equilibria and a natural
toll mechanism, which we call cost-balancing tolls. A set of cost-balancing tolls
turns every path with positive traffic on its edges into a minimum cost path. Hence
any given configuration is induced as a pure Nash equilibrium of the modified
game with the corresponding cost-balancing tolls. We show how to compute in
linear time a set of cost-balancing tolls for the optimal solution such that the total
amount of tolls paid by any player in any pure Nash equilibrium of the modified
game does not exceed the latency on the maximum latency path in the optimal
solution. Our main result is that for congestion games on series-parallel networks
with increasing latencies, the optimal solution is induced as the unique pure Nash
equilibrium of the game with the corresponding cost-balancing tolls. To the best
of our knowledge, only linear congestion games on parallel links were known to
admit optimal tolls prior to this work. To demonstrate the difficulty of computing
a better set of optimal tolls, we show that even for 2-player linear congestion
games on series-parallel networks, it is NP-hard to decide whether the optimal
solution is the unique pure Nash equilibrium or there is another equilibrium of
total cost at least 6/5 times the optimal cost. |