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研究生:梁嘉浚
研究生(外文):Chia-Chun Liang
論文名稱:在希臘神話中尋找賽局的足跡
論文名稱(外文):Seeking footprints of Game theory in Greek mythology
指導教授:周治邦周治邦引用關係
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:國家發展研究所
學門:社會及行為科學學門
學類:綜合社會及行為科學學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:54
中文關鍵詞:希臘神話賽局混合賽局混合策略集體行動
外文關鍵詞:Greek mythologygame theorymixed gamemixed strategycollective action
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本研究採用希臘神話中的故事情節,並套用至混合賽局與集體賽局模型內,藉以觀察故事結果是否能與賽局均衡達成一致,並歸納整理出混合賽局持續進行下之規律,以及各種行動機率變化對賽局均衡之影響。研究結果發現在一般情況下,故事結果與賽局均衡的確出現差異,但若考慮特殊情況下,修正賽局設定後,的確可能發生兩者一致之情況。本研究認為,出現差異的原因在於相關參數的選取與設定,藉由不斷重複的過程中汲取經驗,將參數設定加以修正,便能逐漸減少賽局預測分析上的繆誤。
This research used stories of Greek mythology to explain game theory. By this process, I wished to see if stories’ ending and the equilibrium of game theory were identical, and also tried to find the rules of mixed game.

As a result, I found that stories’ ending and the equilibrium of game theory were different in general situation, but equal in particular situation. The reason for this result is the setting and selection of related parameters. But the variation of game theory can be revised by repeated processes.
目 錄

口試委員會審定書................................................................................i
中文摘要...............................................................................................ii
英文摘要..............................................................................................iii
I. 序論.................................................................................................1
1.1. 研究背景與動機.......................................................................1
1.2. 研究目的...................................................................................3
1.3. 賽局概述...................................................................................3
1.4. 希臘神話...................................................................................5
1.5. 文獻回顧...................................................................................5
1.5.1. Using Greek Mythology to teach Game Theory.............6
1.5.2. Third down with a yard to go..........................................8
1.6. 研究方法...................................................................................9

II. 英雄的決鬥...................................................................................11
2.1. 概論.......................................................................................11
2.2. 神話......................................................................................12
2.2.1. 神話概述:Achilles & Hector的決鬥........................12
2.2.2. 模型設定....................................................................13
2.2.3. 模型結果....................................................................14
2.3. 考慮風險傾向下之模型…………………………….……..30
2.3.1. 模型設定....................................................................30
2.3.2. 模型結果....................................................................31
2.4. 結論.......................................................................................35

III. 將領的抉擇.................................................................................36
3.1. 概論.....................................................................................36
3.2. 神話.....................................................................................37
3.2.1. 神話概述:希臘將領的會議....................................37
3.2.2. 模型設定與分析.....................................................38
3.2.3. 考慮Agamemnon行動下的模型設定與分析........46
3.3. 結論.................................................................................50

IV. 結論.........................................................................................51
參考文獻.....................................................................................53
圖 目 錄

圖1:Beer / quiche game的模型………………………......………….8

圖2:考慮風險下的模型結果…………………………….......……..32

圖3:風險係數改變對高風險行動策略採用機率p的影響..………33

圖4:將領不同選擇下之均衡情況...................................................45

表 目 錄

表2 :成功機率表...............................................................................14

表2- 1:N回合Achilles & Hector擊中身體/頭皆可獲勝的情況......15

表2- 2:N回合Achilles擊中頭/身體,Hector擊中頭可獲勝的情況.15

表2- 3:N回合Achilles擊中頭,Hector擊中身體/頭可獲勝的情況.16

表2- 4:N回合Achilles&Hector擊中頭可獲勝的情況.....................16

表2- 5:N-1回合Achilles & Hector擊中身體或頭皆可獲勝的情況
…………………………………………………………………….....17

表2- 6:N-1回合Achilles擊中頭/身體,Hector擊中頭可獲勝的情況………………………………………………………………….…17

表2- 7:N-1回合Achilles擊中頭,Hector擊中身體/頭可獲勝的情況………………………………………………………………….....18

表2- 8:N-1回合Achilles&Hector擊中頭可獲勝的情況..................19

表2- 9:N-2回合Achilles & Hector擊中身體或頭皆可獲勝的情況
…………………………………………………………………….....20

表2-10:N-2回合Achilles擊中頭/身體,Hector擊中頭可獲勝的情況………………………………………………………………….....20

表2-11:N-2回合Achilles擊中頭,Hector擊中身體/頭可獲勝的情況………………………………………………………………….....21

表2-12:N-2回合Achilles&Hector擊中頭可獲勝的情況………….22

表2-13:若此回合為起始回合下,此賽局的成功機率表………......23

表2-14:代入實際數值的模型結果…………………………………27
Bulfinch, T. (1855). Bulfinch''s mythology. New York : Modern Library.

Berg, J., Dickhaut, J., McCabe, K., (1995). Trust, Reciprocity, and Social History. Games and Economic Behavior, Vol. 10, Iss. 1, p.122-142.

Cho, I-K., and Kreps, D. M., (1987). Signaling Games and Stable Equilibria. Quarterly Journal of Economics, Vol. 102, Iss. 2, p.179-221.

Dixit, A. & Skeath, S., (2004). Games of Strategy (2thed.). New York : W.W. Norton.

Graves, R. (1957). The Greek Myths. Baltimore : Penguin Books.

Grant, S. & Kajii, A. & Polak, B., (2000). Third Down with a Yard to Go: The Dixit-Skeath Conundrum on Equilibria in Competitive Games. Econometric Society World Congress 2000 Contributed Papers 0222, Econometric Society.

Hamilton, E., (1942). Mythology. New York : New American Library.

Lutzker, D. R., (1961). Sex Role, Cooperation and Competition in a Two-Person, Non-Zero Sum Game. Journal of Conflict Resolution, Vol. 5, No. 4, p.366-368.

Moore, J., (1992). Implementation, Contracts, and Renegotiation. Advances in Economic Theory, Vol. 1, p.182-282.

Miller, James D., and Debbie Felton., (2002). Using Greek mythology to teach game theory. American Economist, Vol. 46, Iss. 2, p.69-79.

Mas Colell, A., M. D. Whinston, and J. Green, (1995). Microeconomic theory. New York : Oxford University Press.

Spence, M., (1973). Job market Signaling. Quarterly Journal of Economics, Vol. 87, Iss. 3, p.355-374.

Von Neumann J, Morgenstern O., (1944). Theory of games and economic behavior. New York : Science Editions.
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