Congestion Games: Optimization in Competition

In a congestion game, several players simultaneously aim at allocating sets of resources, e.g., each player aims at allocating a shortest path between a source/destination pair in a given network or, to give another example, each player aims at allocating a minimum weight spanning tree in a given graph. The cost (length, delay, weight) of a resource (edge) is a function of the congestion, i.e., the number of players allocating the resource. In this paper, we survey recent results about the complexity of computing Nash equilibria for congestion games and the convergence time towards Nash equilibria.