應用線性近似法求解Stackelberg對策行為-以路網設計為例

Abstract

競局為常見的群體對策行為，當其跟隨者對於領導者之決策行為的反應函 數是非線性型式時，Stackelberg 競局的均衡解難以求得。Miller 者之 決策行為的線性近似反應函數，但該文中應用的敏感性分析資 漣x境，且 針對不同的Nash均衡點，未重新計算新的敏感性分析資訊，亦為一項缺失 。 坁韘□k克服了Miller所遭遇之問題，成功地構建跟隨者對於領導者之 決策行為的線性近似反應函數。文中並且以複雜之Stackelberg狾′馬牷A 與 MINOS、H-J、IOA、EDO、GSDA痟□桵u性近似法之效能及 晢蚳狺丑A線 性近似法在效能上與先前最具效能之方法相當，在效率則明顯優於先前最 具效率之方法。 b大型實際路網上，將來可朝實証研究繼續發展。本文應 用一階敏感性分析資訊，即已明顯地提高了StackelbergA因此變分不等式 的二階敏感性分析及二次式近似反應函數亦為值得進一步探討之課題。 As Follower's reaction function which responds with Leader's making isn't linear form in Stackelberg game, Solving this difficult. Miller[31] tried to formulate a linear approximation function approximating Follower's real reaction function. The two defects. One is that it cannot find the sensitivity some cases. Another is that the sensitivity information were not each iteration. The Thesis propose a Linear Approximation Algorithm which uses sensitivity analysis to obtain the derivatives of the reaction prevent the shortcomings of Miller' s algorithm. In the article, implemented two examples for our method. The results are put comparison with results of MINOS, H-J, IOA, EDO and GSDA. In our method is as well as the most effective algorithm in the algorithms. In efficiency, LAA is superior to others. In future, extent our method to implement real network and develop quadratic reaction function.