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 在這篇論文中，我們的研究是專注在一種叫道路佔領賽局（route-capturing game）的策略賽局（strategic game）上。在這種賽局中，玩家們用有限的預算競爭一組給定的資源。這種賽局可以用一個圖形（graph）來表示，圖中的端點（vertex）代表玩家，而邊（edge）代表可被佔領的資源。每個玩家都被給予相同的預算，並且可以把這些預算分配在這些邊，以有限的資源，盡可能佔領較多相鄰的邊。針對這樣賽局 我們已經研究了部分種類的納許均衡（nash equilibrium）的存在條件。實驗的結果也展示了這些納許均衡的構造。
 In this thesis,we are concerned with a strategic game called the route-capturing game,in which the players compete for a set of given resources with finite budgets.The game is modeled with a graph,where the vertices stands for the players,and edges stands for the resources to be captured.Given that each player has the same budget and can spends a bounded amount of budget to capture each edge,properties of the Nash equilibria of some classes of the game are investigated.Experimental results are also shown to characterize the constitution of the Nash equilibria.
 中文摘要 i英文摘要 ii誌謝 iii目錄 vi表目錄 viii圖目錄 ix一、緒論 1 1.1 研究背景與動機 1 1.2 符號與術語定義 4 1.3 文獻探討 7二、道路佔領賽局 10 2.1 問題定義 10 2.2 性質 11 2.3 (Kn, C, kC)的納許均衡 14三、實驗結果 20四、結論與未來研究方向 27 4.1 結論 27 4.2 未來研究方向 27參考文獻 29
 [1] K. I. Aardal, S. P. Van Hoesel, A. M. Koster, C. Mannino, and A. Sassano, "Models and Solution Techniques for Frequency Assignment Problems," Annals of Operations Research, vol. 153, no. 1, pp. 79--129, 2007.[2] M. Beckmann, C. McGuire, and C. B. Winsten, "Studies in the Economics of Transportation," RAND Corporation, Tech. Rep., 1956.[3] O. Berman and M. Cutler, "Resource Allocation During Tests for Optimally Reliable Software," Computers & Operations Research, vol. 31, no. 11, pp. 1847--1865, 2004.[4] Y.-H. Chang, "New Efficient Encoding Method of Genetic Algorithms for Resource/Production Allocation Problems," Ph.D. Dissertation, National Central University, 2003.[5] Y. Dai, M. Xie, K. Poh, and B. Yang, "Optimal Testing Resource Allocation with Genetic Algorithm for Modular Software Systems," Journal of Systems and Software, vol. 66, no. 1, pp. 47--55, 2003.[6] G. Dan, "Cache-to-Cache: Could ISPs Cooperate to Decrease Peer-to-Peer Content Distribution Costs?" IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 9, pp. 1469--1482, 2011.[7] E. Gelenbe and H. Shachnai, "On g-Networks and Resource Allocation in Multimedia Systems," European Journal of Operational Research, vol. 126, no. 2, pp. 308--318, 2000.[8] M. M. Halldorsson and G. Kortsarz, "Tools for Multicoloring with Applications to Planar Graphs and Partial k-trees," Journal of Algorithms, vol. 42, no. 2, pp. 334--366, 2002.[9] H. Huang, B. Zhang, S.-H.G. Chan, G. Cheung, and P. Frossard, Coding and Replication Co-Design for Interactive Multiview Video Streaming. Proceedings IEEE INFOCOM, 2012.[10] R. Johari and J. N. Tsitsiklis, "A Scalable Network Resource Allocation Mechanism with Bounded Efficiency Loss," IEEE Journal on Selected Areas in Communications, vol. 24, no. 5, pp. 992--999, 2006.[11] F. P. Kelly, A. K. Maulloo, and D. K. Tan, "Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability," Journal of the Operational Research Society, vol. 49, no. 3, pp.237--252, 1998.[12] F. H. Knight, "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, vol. 38, no. 4, pp. 582--606, 1924.[13] A. Leff, J. L. Wolf, and P. S. Yu, "Replication Algorithms in a Remote Caching Architecture," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 11, pp. 1185--1204, 1993.[14] A. Lova, C. Maroto, and P. Tormos, "A Multicriteria Heuristic Method to Improve Resource Allocation inMultiproject Scheduling," European Journal of Operational Research, vol. 127, no. 2, pp. 408--424, 2000.[15] A. Mas-Collel, M. D. Whinston, and J. Green, Microeconomic Theory. Oxford University Press , 1995.[16] H. Moulin, "The Price of Anarchy of Serial, Average and Incremental Cost Sharing," Economic Theory, vol. 36, no. 3, pp. 379--405, 2008.[17] R.B. Myerson, Game Theory: Analysis of Conflict. Harvard University Press, 1997.[18] L. Narayanan, "Channel Assignment and Graph Multicoloring," Handbook of Wireless Networks and Mobile Computing, pp. 71--94, 2002.[19] J. F. Nash, "Equilibrium Points in n-Person Games," Proceedings of the National Academy of Sciences, vol. 36, no. 1, pp. 48--49, 1950.[20] J. von Neumann, "Zur Theorie Der Gesellschaftsspiele," Mathematische Annalen, vol. 100, no. 1, pp. 295--320, 1928.[21] W. Novshek, "On the Existence of Cournot Equilibrium," The Review of Economic Studies, vol. 52, no. 1, pp. 85--98, 1985.[22] V. Pacifici and G. Dan, "Convergence in Player-Specific Graphical Resource Allocation Games," IEEE Journal on Selected Areas in Communications, vol. 30, no. 11, pp. 2190--2199, 2012.[23] R. Ramanathan and L. Ganesh, "Using AHP for Resource Allocation Problems," European Journal of Operational Research, vol. 80, no. 2, pp. 410--417, 1995.[24] R. W. Rosenthal, "A Class of Games Possessing Pure-Strategy Nash Equilibria," International Journal of Game Theory, vol. 2, no. 1, pp. 65--67, 1973.[25] T. Roughgarden, Selfish Routing and the Price of Anarchy. The MIT Press, 2005.[26] J. M. Smith and G. Price, "The Logic of Animal Conflict," Nature, vol. 246, p. 15, 1973.[27] R. Srikant, The Mathematics of Internet Congestion Control. Birkhauser Boston, 2004.[28] E. Zermelo, Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of the Fifth International Congress of Mathematicians. Cambridge University Press, 1913.
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 1 線上社群網路之訊息擴散賽局模型分析

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 1 基於賽局理論之計程車共乘推薦機制 2 韓美自由貿易協定談判之分析：雙層賽局理論的觀點 3 應用賽局理論探討白地策略之個案研究 －以統一超商為例 4 以賽局理論探討單一零售商與單一供應商之供應鏈協同存貨之研究 5 家族企業商標爭奪之賽局分析 6 酒駕事件之賽局分析 7 酒吧賽局中出席行為之實驗研究 8 利他懲罰與抗議訊息在最後通牒賽局中對決策的影響 9 以賽局理論為基礎之工程教育合作學習 10 從賽局理論看鬥智作品的邏輯基礎 11 以合作賽局看合作聯盟-以Garmin與Asus為例 12 群組規模與資訊揭露對協同行為之影響:酒吧賽局之實驗研究 13 內線交易可罰性基礎及現行規範效果分析──以賽局論為中心 14 以非合作式賽局理論分析中華郵政導入無線射頻辨識系統 15 基於賽局理論的合作學習融入國小閱讀理解成效之研究

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