Advances in Dynamic Traffic Assgmnt: TAC A New Relationship Between Wardrop's User Equilibrium and Nash Equilibrium

作者：Jin Wen Long^*

来源：Networks and Spatial Economics, 2015, 15(3): 617-634.

DOI：10.1007/s11067-014-9250-x

• Asymmetric traffic assignment problems
• Wardrop's user equilibrium
• Finite non-cooperative games
• Nash equilibrium
• Fixed-point formulation
• Existence of user equilibrium

Traditionally traffic assignment problems (TAPs) have been formulated as non-cooperative games (NCGs), and Wardrop's user equilibrium (UE) of a TAP as Nash equilibrium (NE) of the corresponding NCG. In this study, in contrast, we propose a mapping from finite NCGs (F-NCGs) to asymmetric TAPs (A-TAPs) on a two-way or urban network, in which the travel cost of one link depends on flows on other links. With the help of three route-based formulations of UE, we show that NE of an F-NCG is equivalent to UE of the corresponding A-TAP. Based on the new relationship, we extend Nash's fixed point formulation of NE to prove the existence of static UE. This study provides a more complete picture of the relationships between NCGs and TAPs. In the future we will be interested in studying Nash's fixed point formulation for dynamic UE.

• 出版日期2015-9