在此篇論文中，我們將兩種基本的團體賽制轉化為策略賽局
以及廣域賽局，並使用賽局理論來分析團體賽中的排點機制。此
外，我們也可以利用賽局中的納許平衡來優化排點。再者，為了
捕捉教練們對各種贏法的偏好，我們進而提供了三種參入權重因
子的模型。在模擬的部份，我們蒐集了星海爭霸中兩大團體賽的
資料，用以展現我們提出模型的潛能。

In this paper, we formulate the two basic team competition systems
into the strategic and the extensive games, which allow us to use game
theoretic approach to analyze the scheduling of matches. Furthermore,
we can find the Nash equilibrium and the subgame perfect equilibrium as
a way to optimize the strategies for athletes designating problem. Also,
in addition to model the coaches’ preferences, three weighted versions of
the original model are provided in the later section. In the simulations,
wecollecttwomajorteamcompetitiondataofStarCraftIItodemonstrate
the potential of the proposed method.

中 文 摘 要 i
Abstract ii
Acknowledgements iii
List of Figures vi
List of Tables vii
1 Introduction 1
2 A Strategic Game Formulation 4
2.1 Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . 7
3 An Extensive Game Formulation 13
3.1 Subgame Perfect Equilibrium . . . . . . . . . . . . . . . 16
3.2 Analysis of Match 2 . . . . . . . . . . . . . . . . . . . . 17
3.3 Analysis of Match 1 . . . . . . . . . . . . . . . . . . . . 22
4 Two Hybrid Competition Systems 26
4.1 Proleague Format . . . . . . . . . . . . . . . . . . . . . 26
4.2 Taiwan eSports League(TeSL) Format . . . . . . . . . . 28
5 Weighted Version 31
5.1 Model 1 and Model 2 . . . . . . . . . . . . . . . . . . . 31
5.2 Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6 Numerical Results 41
6.1 Strategic game simulation . . . . . . . . . . . . . . . . . 42
6.2 Extensive game simulation . . . . . . . . . . . . . . . . 47
7 Conclusion 52
8 Appendix 54

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