Utility Allocation of Sports Management Under Uncertainty: Dividend Approach Viewpoint

不確定狀況下運動管理的效能分配：利能過程觀點

10.6162/SRR.201806_145.0005

廖于賢(Yu-Hsien Liao)；陳坤檸(Kun-Ning Chen)；林新龍(Hsing-Lung Lin)；紀恩成(En-Cheng Chi)

game theory ； Shapley value ； potential approach ； interval transferable-utility games ； 賽局理論 ； 夏普利值 ； 位能過程 ； 區間利益可交換賽局

大專體育

145期（2018 / 06 / 30）

39 - 46

英文

In general, game theory is an academic field that applies pure mathematical results to the analysis of various interaction relationships and related models among agents and coalitions. In addition to theoretical analysis, game-theoretical results could also be adopted to provide optimal conditions and equilibrium for real-world models. In particular, improvements in the efficiency of sports management could potentially be realized by applying the theoretical results from analyses of various other fields. Therefore, the purpose of this paper is to adopt some game-theoretical results to investigate the relations among some results of the interval Shapley value and the field of sports management. The main investigative steps are as follows: (1) We introduced basic mathematical models of game theory under uncertainty, and extended these models to the framework of sports management. (2) Different from the potential approach on interval transferable-utility games, we adopted the dividend approach to provide an alternative viewpoint for the interval Shapley value. Further, we applied the dividend approach to show that the interval Shapley value satisfies consistency. (3) The real-world relevance of this approach and related game-theoretical results can be confirmed by some results related to management science. (4) Finally, we applied these game-theoretical results of the interval Shapley value to the framework of sports management. We conclude that the interval Shapley value can be applied to the field of sports management. The extended suggestions also pointed out that other game-theoretical methods under uncertainty may be applied to the field of sports management.

一般來說，賽局理論是一門利用純數學結果來分析個體與團體間各種互動現象及相關模型的領域。除了理論的分析，也被廣泛的應用在尋求各種現實世界模型的均衡與最佳化。而在運動管理的領域，近來也開始運用各項其他領域的理論結果來提升運動管理效能。因此，本文目的著重於利用一些賽局理論的結果去探討區間夏普利值與運動管理領域之間的關係。主要的研究步驟如下：一、我們在不確定性的狀況下引進一些基本的數學賽局理論模型，並且將這些模型拓展應用到運動管理的範疇。二、有別於區間利益可交換賽局上的位能過程，我們利用利能過程來對區間夏普利值提出不一樣的觀點。接著也藉由利能過程來證明區間夏普利值符合一致性。三、這個利能過程將被一些現實世界中關於管理科學的結果賦予現實的相關意義。四、最後，我們將區間夏普利值的相關理論結果拓展應用到運動管理的架構。所得結語指出本文證明區間夏普利值可以被拓展應用到運動管理的領域，藉此提升運動管理效能。尤有甚者，所衍生出來的建議也指出其他具有不確定性的賽局理論方法或許也可以被應用到運動管理的領域。

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