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Abstract
A variational inequality (VI) formulation of a mixed traffic assignment problem associated with user equilibrium (UE) player and altruistic players (UE-AP) is developed. The users governed by the UE player use the paths with minimum actual travel cost, while the users governed by altruistic players use the paths with minimum perceived travel cost, which is a linear combination of the actual and marginal travel costs. A nonlinear programming method is adopted to derive the efficiency loss of the UE-AP mixed equilibrium with polynomial cost function. Finally, numerical examples are given to verify our analytical results.
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