本論文主旨是以一個闡述性範例給予擴展式賽局及納許平衡點的介紹。這個範例描述兩個零售商(如統一超商及全家超商)間的競爭並分析他們的策略以銷售新產品。此賽局已非合作性方式形成。為了使賽局論抽象的公理化形式更具體，我們使用這個範例來闡述一個給定的非合作賽局的架構。最後，我們回來檢視那許在1950 及1951 年有關納許平衡點存在性的工作，並把它呈現為Kakutani 及Brouwer 固定點定理的應用結果。由於近日納許的意外驟逝，我們以在此論文中
對賽局的探討紀念他。

The main purpose of this thesis is to give an introduction to games in extensive form and its Nash equilibrium throughout an illustrative example. The example describes the competition between two retailers, say 7-Eleven and FamilyMart, for their strategies to sell a new product. We formulate it as a non-cooperative game. In the attempt to make the abstract axiomatic approaches to the game theory more transparent and concrete, we use this example to illustrate the structure of a given
non-cooperative game. Finally, we pay a revisit to Nash's work in 1950 and 1951
about the existence of Nash equilibrium and also show the results as consequences of
Kakutani and Brouwer's fixed point theorems. In the wake of Nash's death in a car
accident recently, we present our understanding toward the game theory in this thesis
as our way to remember him.

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