This study makes a unique contribution to applied game theory and to the studies of Shiji (Records of Grand Historian) and the Warring States Period of ancient China (453-221B.C.) by constructing and analyzing the annual series of alliance structures or partitions of the seven states during the period of two hundred thirty three years. It shows that twenty six of the eight hundred seventy seven possible partitions were observed, and that the three most frequent partitions were the finest partition (146 years), partitions with four singletons and one three-member coalition (63 years), and partitions with five singletons and one two-member coalition (33 years). Such quantitative results have future applications in alliance studies, game theory, and international economics. They also provide a list of future research topics such as the unknown statistical properties of a series of partition of seven elements with 233 observations.

我們建立一個無窮多期的三人賽局，嘗試討論歷史上著名的合縱與連橫同盟策略。每位參賽者可以選擇自己的同盟對象，以增加最後獲勝的機率。我們從同時移動的賽局結構中，得到合縱策略(實力較弱的參賽者之間同盟)與連橫策略(與實力最強的參賽者同盟)均存在於混合策略。這將有助於同時解釋三國赤壁之戰的同盟、南宋與蒙古同盟等歷史事件。 / This paper will study a three-player game with infinite periods where each player decides whether to league together to increase his winning rate. We discuss which one will be chosen to be the member of leagues. The results show that Hezong and Lianheng both exist in mixed strategy Nash equilibriums of simultaneous move game. It is possible that the fall of Jin and the Battle of Red Cliffs in Chinese history were just coincident or random events. Furthermore the players usually have a tendency to be in league with the strongest.