以多層級貝氏賽局為基礎之感知無線網路頻譜買賣

Abstract

在本篇論文，我們以賽局理論的角度來研究感知無線電網路頻譜買賣。我們考慮一個由多主要服務者(primary service)和多的次要服務者(secondary service)所構成的感知無線電網路。主要服務者是此買賣賽局中的頻譜賣家，它們可以設定租借頻帶給次要服務者的單位頻帶價格；次要服務者是該賽局中的買家，它們要決定跟買家買多少頻帶。我們提出以多層級貝氏賽局為基礎的買賣模型來建立每個玩家可能未公開的私人資訊的情況，並在符合頻帶限制下依序地求得完美貝氏平衡點(perfect Bayesian equilibrium)。所謂的頻帶限制其實就是所有買家所要求的頻帶量加起來不能超過賣家所能負荷，而每個買家所要求的頻帶量也不能是負值。由倒推歸納原則，我們將買家的Karush-Kuhn-Tucker (KKT) condition轉化為賣家的最佳化問題之條件，並將所有賣家的KKT condition集合起來成為joint KKT condition，符合該joint KKT condition的解即為此賽局的解。我們並提出以active-set algorithm來解該joint KKT condition，並分析它的複雜度。此論文也探討了玩家的行動和對未知資訊的信念是否會收斂。在模擬中，我們比較了我們的作法和前人的作法，並且數值上探討了該賽局之收斂行為。

In this thesis, we study the problem of spectrum trading in cognitive radio (CR) networks from a game theoretical perspective. Particularly, we consider a CR network with multiple primary services (PSs) and multiple secondary services (SSs), where all PSs are sellers targeting at setting the prices for spectrum leasing and SSs are buyers deciding how much spectrum are demanded from each PS in the trading game. Aiming at dealing with the trading behaviors, we propose using a multistage Bayesian game based trading model to account for possible unknown private information in each player, and obtain the perfect Bayesian equilibrium (PBE) sequentially under a bandwidth constraint, which requires all SSs' demanded bandwidth not exceeding that the PS can possibly offer and each SS's demand should not be negative. Following the backward induction principle, we transfer the Karush-Kuhn-Tucker (KKT) condition of the SSs into each PS's optimization constraint, and collectively form joint KKT conditions that satisfy the bandwidth constraint. We present an active-set based algorithm to solve the joint KKT conditions, and analyze the corresponding complexity. Furthermore, the convergence behaviors of the action profiles and the beliefs of the unknown information are also investigated in the work. Finally, in the simulations, we compare the proposed approach with earlier work and numerically study the convergence behaviors of the proposed multistage game.