On the Cause of the Civil War between Caesar and Pompey from the Perspective of Game Theory

Abstract

Game Theory is an emerging branch of applying mathematics and is applied to various fields of researches to explain social phenomena. This paper employed game theory to explicate the civil war between Caesar and Pompey. Caesar was a famous commander during the twilight of Roman Republic. He conquered Gaul and was elected as the Consul of Rome for two times. Pompey was a famous politician and commander and was contemporary to Caesar. He led Rome's military operations during the third Mithridatic War and defeated Pontus. Then he wiped out all the pirates in Mediterranean Sea. As the leader of patrician republicans, he was the major political rival of Caesar. The civil war between them had a major impact on Rome history: the aristocratic Republic was broken down and the path to the Empire - the rule of one man- was clear.

This paper applied the game theory to analyze what caused the war between Pompey and Caesar. The conflict between these two could be theorized in a model of Prisoner's Dilemma; their strategies were considered as common knowledge; their conflict began with the death of Crassus and reached its climax in the beginning of the war, which was regarded as a dynamic game; the breaking out of this war was regarded as a Nash Equilibrium.

The purpose of this paper is to explain what caused the war between Pompey and Caesar under the game theory. The conclusion is that the civil war was the result of rationality of both sides.

Key Words: game theory, Caesar, Pompey, civil war

摘        要

博弈论是应用数学的一个新近产生的分支，被广泛用于各种研究中，用来解释社会现象。本文尝试用博弈论来解释凯撒与庞培之间的内战的原因。凯撒是罗马共和国后期著名统帅、军事家，征服了高卢，两次当选执政官；庞培是罗马共和国后期政治家、统帅，主导了第三次米特拉达蒂战争，击败了本都，打败了横行于地中海的海盗，是贵族共和派的领袖，凯撒的主要政治对手。他们的内战导致了贵族共和国的最终瓦解和帝国（一人之治）的兴起，对于罗马有重大历史意义。
本文从博弈论的角度出发对凯撒与庞培内战爆发的原因做出分析。其两人的冲突，可以简化为一个囚徒困境的模型；他们的策略，可以看做公共知识；他们的矛盾冲突从克拉苏之死即开始，直到内战爆发，可以看做重复博弈；而内战的最终爆发，可以看做一个纳什均衡。
本文的目的在于从博弈论的角度对凯撒与庞培内战爆发的原因做出分析，并得出以下结论：内战是双方理性选择的必然结果。

关键词：博弈论，凯撒，庞培，内战