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| Title: | 再探極小極大理論在網球比賽的應用：發球及接球能力如何影響選手的發球策略
Minimax Play in Tennis Revisited : How Serving and Returning Abilities Affect Players’ Strategic Behavior |
| Authors: | 莊品珊
Chuang, Pin Shan |
| Contributors: | 張元晨
Chang, Yuan Chen
莊品珊
Chuang, Pin Shan |
| Keywords: | 賽局理論
極大極小理論
網球實證
Game Theory
Minimax
Empirical research of tennis |
| Date: | 2016 |
| Issue Date: | 2017-10-02 10:14:21 (UTC+8) |
| Abstract: | 這篇論文參考Walker and Wooders (2001)的網球發球模型，並且使用較完整的網路社群記錄的網球比賽資料庫，檢驗網球選手的發球決策是否符合賽局理論中的混合策略理論預測的行為模式。Walker and Wooders (2001)提到要檢視混合策略是否成立，必須通過兩個假設檢定。第一個是無論發球的方向為何，發球的勝率均相等。第二個是發球的方向必須符合序列不相關。
相較先前的論文，我們更改了發球方向和分數的紀錄方式，使資料更符合比賽實際的情形。另外，我們使用了ATP網站上的排名，依發球者和接球者的能力排名將比賽區分為四個子集合，為的是觀察對戰組合對選手策略行為上的影響。
實證結果顯示，當在接發球者能力都很強的比賽中，混和策略並不成立。相對地，其他三個子集合中都符合理論預期。在序列不相關的檢定中，發球能力差的選手容易出現過度變換方向的情形，此可能因為選手要以不可預測來彌補發球能力的不足。另一方面，在好的發球者的比賽中，被拒絕的序列不相關檢定都是源自過少的方向變換，我們推斷因為發球者的發球品質好，所以更能著重於攻擊對手的弱點而非讓對手無法預測發球落點。
Using the tennis serving model introduced by Walker and Wooders (2001) and a more comprehensive database obtained from a tennis charting program, we test whether professional tennis players behave according to the predictions of the mixed strategy. We test two predictions from Walker and Wooders (2001) model: the hypothesis for equality of winning probability and serial independence. We improve the method of recording each point in matches and use the rank (serving rank and returning rank) from ATP leaderboards to separate our data to four subsets. We hypothesize that rivalry combination may have impact on the strategic behavior of players. Our empirical result shows that players don’t play mixed strategy in the top-ranking server vs. top-ranking receiver subset, while players conform to what theory suggests for the other subsets. On the other hand, run-test results show that poor servers tend to switch serving directions too often, probably to defend their weakness by creating more uncertainties in serves. However, good servers do not have this tendency because of their high serving quality. |
| Reference: | Bailey, B. J., & McGarrity, J. P. (2012). The effect of pressure on mixed-strategy play in tennis: The effect of court surface on service decisions. International Journal of Business and Social Science 3(20), 11-18.
Chiappori, P. A., Levitt, S., & Groseclose, T. (2002). Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. American Economic Review 92:1138-1151.
Gauriot, R., Page, L., & Wooders, J. (2016). Nash at Wimbledon: Evidence from Half a Million Serves. Working paper.
Hsu, S. H., Huang, C. Y., & Tang, C. T. (2007). Minimax play at Wimbledon: comment. The American Economic Review 97(1), 517-523.
O`Neill, B. (1987). Nonmetric test of the minimax theory of two-person zerosum games. Proceedings of the National Academy of Sciences 84(7), 2106-2109.
Palacios-Huerta, I. (2003). Professionals play minimax. The Review of Economic Studies 70(2), 395-415.
Rowe, C. (2013). Testing the Minimax Theorem in the Field: The Interaction between Pitcher and Batter in Baseball. Working paper.
Spiliopoulos, L. (2016). Minimax Play at Wimbledon Redux. Working paper.
Walker, M., & Wooders, J. (2001). Minimax play at Wimbledon. The American Economic Review 91(5), 1521-1538.
Wiles, J. (2006). Mixed Strategy Equilibrium in Tennis Serves. Working paper. |
| Description: | 碩士
國立政治大學
財務管理研究所
104357027 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0104357027 |
| Data Type: | thesis |
| Appears in Collections: | [財務管理學系] 學位論文
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| 702701.pdf | 1331Kb | Adobe PDF2 | 15 | View/Open |
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