路網指派賽局之非合作性質

Abstract

交通指派是運輸規劃過程中重要的一環，透過指派模式所預測出的路網流量，對於運輸管理的決策是重要的參考指標。目前交通指派模式的發展已趨於成熟，透過Wardrop的道路行為準則，交通指派模式利用各種數學理論被寫成各種問題，包括數學規劃問題、非線性互補問題、變分不等式問題、不動點問題等均衡指派模式。近年來由於賽局理論的發展，交通問題開始以賽局的觀點來討論，透過兩人賽局的概念，更有雙層規劃模式的產生。 本研究利用使用者均衡的行為準則，以賽局理論的視角與定義，構建一n人的非合作凹性賽局，證明其唯一性與存在性，並推導其與傳統的靜態均衡指派變分不等式模型之間的關聯性。最後利用Zukhovitsky對賽局的假設，證明此n人路網賽局的解，相當於解一兩人零和賽局的解。此一概念對於雙層規劃模式在路網指派的運用為一重要的根據。

Traffic assignment is one of the important part of transportation planning procedure. Though assignment model, we can predict the network flow which is the vital norm for decision-making of transportation management. Traffic assignment model already tends to be mature at present. Based on the principle proposed by Wardrop, traffic assignment problem are formulated in different formulation by several mathematical theory, includes Mathematical Programming problem, Nonlinear Complementarity Problem, Fixed-Point Problem, and Variational Inequality Problem. This research based on the concept of user equilibrium, construct a n-person non-cooperative concave game, and demonstrate the relation with the static equilibrium assignment model through the variation inequality form. In the latest part of the paper use the assumption proposed by Zukhovitsky to prove the equivalent between n-person concave game and two-person zero-sum game. The demonstration process help us analysis the assignment problem in different view and the proof of equivalent simplify the problem and help us solve problem in easily way.