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

The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against “analytic narratives”, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling.