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We study a heterogeneous routing game in which vehicles might belong to morethan one type. The type determines the cost of traveling along an edge as afunction of the flow of various types of vehicles over that edge. We relax theassumptions needed for the existence of a Nash equilibrium in thisheterogeneous routing game. We extend the available results to presentnecessary and sufficient conditions for the existence of a potential function.We characterize a set of tolls that guarantee the existence of a potentialfunction when only two types of users are participating in the game. We presentan upper bound for the price of anarchy (i.e., the worst-case ratio of thesocial cost calculated for a Nash equilibrium over the social cost for asocially optimal flow) for the case in which only two types of players areparticipating in a game with affine edge cost functions. A heterogeneousrouting game with vehicle platooning incentives is used as an examplethroughout the article to clarify the concepts and to validate the results.

A Necessary and Sufficient Condition for the Existence of Potential Functions for Heterogeneous Routing Games