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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 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.
Keywords: Napoléon; Blücher; Grouchy; Waterloo; military history; rational choice theories; game theory; zero-sum two-person games; analytical narrative; (follow links to similar papers)
JEL-Codes: B49; C72; N43; (follow links to similar papers)
44 pages, April 1, 2009
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