A Quantitative Study of Alliance Structures in the Warring States of Ancient China, 453-221 B.C.

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