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Differential stackelberg games and their application to dynamic pricing, production planning network design, and logistics.

機譯：差分Stackelberg游戲及其在動態(tài)定價，生產(chǎn)計劃網(wǎng)絡設計和物流中的應用。

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摘要

Recently, Stackelberg games have been employed by many economists who use game theory concepts to solve dynamic competitive service sector problems such as dynamic pricing, production planning, logistics, supply chain management, and transportation network flow prediction and control. Hence, Stackelberg games have become the focus of much research activity.;In this thesis, we provide a framework for studying player interaction based on the Stackelberg- Cournot-Nash behavioral assumption. We briefly review the classical theory of dynamic Stackelberg games, and show how the Nash equilibrium of a lower level problem may be better described by so-called differential variational inequalities (DVI). We also show that when each agent in the lower level problem is solving a stochastic optimal control with a linear quadratic form, the stochastic Nash equilibrium can be expressed as a Riccati system of equations. Both a DVI formulation and a Riccati system of equations may be used to express the solution of the lower level problem implicitly as a function of the upper level problem's controls. Hence, we are able to convert the bi-level optimization problem into a single-level problem. Furthermore, we study the application of differential Stackelberg games on two different areas: freight transport, and strategic pricing and revenue management. In the first model, we con- sider a Stackelberg game between a single carrier that acts as the leader and multiple shippers involved in a Nash competition. In the second model, we study the interaction between a supplier who is the leader and multiple retailers who are competing to sell a homogeneous commodity in a market when the market price evolves based on an Ito-type stochastic process.
機譯：最近，Stackelberg游戲已被許多經(jīng)濟學家所采用，他們使用博弈論的概念來解決動態(tài)競爭性服務部門的問題，例如動態(tài)定價，生產(chǎn)計劃，物流，供應鏈管理以及運輸網(wǎng)絡流量的預測和控制。因此，Stackelberg游戲已成為許多研究活動的重點。本文為基于Stackelberg-Cournot-Nash行為假設的玩家互動研究提供了一個框架。我們簡要回顧了動態(tài)Stackelberg博弈的經(jīng)典理論，并展示了如何通過所謂的差分變分不等式（DVI）更好地描述較低水平問題的納什均衡。我們還表明，當較低級問題中的每個主體都正在求解具有線性二次形式的隨機最優(yōu)控制時，隨機Nash平衡可以表示為Riccati方程組。 DVI公式和Riccati方程組都可以用來隱式地表達下層問題的解，作為上層問題控制的函數(shù)。因此，我們能夠?qū)杉墐?yōu)化問題轉(zhuǎn)換為單級問題。此外，我們研究了差分Stackelberg游戲在兩個不同領(lǐng)域的應用：貨運，戰(zhàn)略定價和收益管理。在第一個模型中，我們考慮了充當領(lǐng)導者的單個承運人與參與納什競賽的多個托運人之間的Stackelberg游戲。在第二個模型中，我們研究了當市場價格基于伊藤型隨機過程而變化時，作為領(lǐng)導者的供應商與競爭在市場上出售同類商品的多個零售商之間的相互作用。

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  • 作者

    Meimand, Amir H.;

  • 作者單位

    The Pennsylvania State University.;

  • 授予單位 The Pennsylvania State University.;
  • 學科 Operations research.;Mechanical engineering.
  • 學位 Ph.D.
  • 年度 2013
  • 頁碼 172 p.
  • 總頁數(shù) 172
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類
  • 關(guān)鍵詞

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