Maximum Congestion Games on Networks: How Can We Compute Their Equilibria?

We study Network Maximum Congestion Games, a class of network games where players choose a path between two given nodes in order to minimize the congestion of the bottleneck (the most congested link) of their path. For single-commodity games, we provide an algorithm which computes a Pure Nash Equilibrium in polynomial time. If all players have the same weight, the obtained equilibrium has optimum social cost. If players are allowed to have different weights, the obtained equilibrium has social cost at most 4 3 times worst than the optimum. For multi-commodity games with a fixed number of commodities and a particular graph topology, we also provide an algorithm which computes a Pure Nash Equilibria in polynomial time. We also study some issues related to the quality of the equilibria in this kind of games.