Potential in congestion game with different types of vehicles

Abstract

Heterogeneous congestion games make it possible to simulate traffic situations involving multiple classes of vehicles with different preferences in choosing routes. In the presented work, we prove the existence of a potential in a discrete congestion game with $n$ classes of players. Examples are given of calculating equilibria and the emergence of the Braess paradox, as well as the use of the constructed congestion game to analyze the distribution of vehicles in the graph of urban roads of the city of Petrozavodsk.