A Game-Theoretic Analysis of the Waterloo Campaign and Some Comments on the Analytic Narrative Project

Abstract: The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modelling of Napoléon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoléon made on 17 June 1815 to detach part of his army and send it against the Prussians, whom he had defeated, though not destroyed, on 16 June at Ligny. Military strategists and historians agree that this decision was crucial but disagree about whether it was rational. Hypothesizing a zero-sum game between Napoléon and Blücher, and computing its solution, we show that dividing his army could have been a cautious strategy on Napoléon’s part, a conclusion which runs counter to the charges of misjudgment commonly heard since Clausewitz. On the other hand, the paper addresses some methodological issues relative to “analytic narratives”. Some political scientists and economists who are both formally and historically minded have proposed to explain historical events in terms of properly mathematical game-theoretic models. We liken the present study to this “analytic narrative” methodology, which we defend against some of objections that it has aroused. Generalizing beyond the Waterloo case, we argue that military campaigns provide an especially good opportunity for testing this new methodology.