Efficiency Loss of UE-CN Mixed Equilibrium Traffic Assignment under Road Pricing

The efficiency loss of two kinds of player (UE player and CN players) traffic assignment under road pricing is investigated, the users under UE player aim to minimize her/his own travel cost, the users belonging to the same CN player can fully cooperate with each other and different players will fully compete with each other, The users of one CN player aim to minimize their own total travel cost while compete with users of other players. Firstly, a variational inequality (VI) model is established to describing this mixed routing game. Then, the upper bound of UECN mixed equilibrium traffic assignment is derived by analytic derivation when the road pricing is consider as (not consider as) part of total travel costs, respectively. Results show that the upper bound is a constant when road pricing is considered as part of total travel costs and the link travel cost functions satisfy some given conditions. The upper bound depends on the class of link travel cost functions and the road pricing scheme when road pricing is not considered as part of total travel costs.