On Braess’ paradox and average quality of service in transportation network cooperative games

In the theory of congestion games, the Braess’ paradox shows that adding one resource to a network may sometimes worsen, rather than improve, the overall network performance. Here the paradox is investigated under a cooperative game-theoretic setting, in contrast to the non-cooperative one typically adopted in the literature. A family of cooperative games on networks is considered, whose utility function, defined in terms of a traffic assignment problem and the associated Wardrop equilibrium, expresses the average quality of service perceived by the network users.