本文旨在探討團體職業球隊競賽中,主場收益分享比例的調整如何影響球隊間相對戰力,是否能促進戰力均衡發展之議題。
Szymanski and K´esenne (2004)認為收益分享越平均越會導致戰力更不均衡。
然而其主場收益函數只受球隊獲勝率的影響,本文另外考量總才能投入的影響,擴充其原模型進行研究。
我們發現,在創造收益的先天條件給定時,球隊總才能投入對收益的影響只要大於一定之臨界值,就足以導致收益分享越平均戰力越均衡的結果。
當然,這結果的實現空間,會隨著對戰兩球隊創造收益的先天條件不對稱而有所差別。

The purpose of this thesis is to investigate how the revenue sharing rule affects competitive balance between teams in a group professional contest.
Szymanski and K´esenne (2004) asserts that the more average revenue sharing the more uneven competitive balance.
However, in the model, the revenue generated from the home match is determined only by win percentage of the home team.
In addition to that, the thesis considers impacts of the total talent investments by the matching teams on the revenue.

It finds out that, given congenital conditions to generate revenue,
it may result in a situation that the more average revenue sharing the more even competitive balance,
as long as the impact parameter of the total talent investments is over a threshold.
Of course, the parameter space that supports the result varys with the degree of congenital asymmetry to generate revenue between the teams.

1 緒論1
1.1 研究動機. . . . . . . . . . . . . . . . . . . . 2
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . 4
1.3 研究方向. . . . . . . . . . . . . . . . . . . . 7
2 Szymanski and K´esenne (2004)
原始模型11
2.1 原始模型的設定. . . . . . . . . . . . . . . . 11
2.2 收益分享對戰力均衡的影響之推導. . . . . . 15
2.3 特定形式主場收益函數的例子. . . . . . . . 18
3 考慮競賽球隊總才能投入對收益
之影響的擴充模型20
3.1 擴充模型之收益函數. . . . . . . . . . . . . 20
3.2 收益分享對戰力均衡的影響之推導. . . . . . 22
3.3 特定形式收益函數下的擴充模型. . . . . . . 25
3.4 吸引力優勢( σ ) 和總才能投入對收益的影
響( θ ) 之合理空間. . . . . . . . . . . . . . 26
3.5 總才能投入對收益的影響( θ ) 變動時,
分享比例對球隊間相對戰力的影響. . . . . . 29
3.6 相對戰力恆定中的σ 與θ 之關係. . . . . . . 32
3.7 收益分享越平均越能促進戰力均衡的參數空間37
3.8 小結. . . . . . . . . . . . . . . . . . . . . . 39
4 結論42
參考文獻47

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