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A game theoretic analysis of the Waterloo campaign and some comments on the analytic narrative project

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  • Mongin, Philippe

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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.

Suggested Citation

  • Mongin, Philippe, 2009. "A game theoretic analysis of the Waterloo campaign and some comments on the analytic narrative project," Les Cahiers de Recherche 915, HEC Paris.
  • Handle: RePEc:ebg:heccah:0915
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    File URL: http://www.hec.fr/var/fre/storage/original/application/dce1d70d3ee3305fdeda9bafef908dd2.pdf
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    References listed on IDEAS

    as
    1. O. G. Haywood, 1954. "Military Decision and Game Theory," Operations Research, INFORMS, vol. 2(4), pages 365-385, November.
    2. Brams, Steven J., 2012. "Game Theory and the Humanities: Bridging Two Worlds," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262518252, January.
    3. Philippe Mongin, 2006. "Value Judgments and Value Neutrality in Economics," Economica, London School of Economics and Political Science, vol. 73(290), pages 257-286, May.
    4. Robert H. Bates & Avner Greif & Margaret Levi & Jean-Laurent Rosenthal, 1998. "Analytic Narratives," Economics Books, Princeton University Press, edition 1, number 6355.
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    More about this item

    Keywords

    Napoléon; Blücher; Grouchy; Waterloo; military history; rational choice theories; game theory; zero-sum two-person games; analytical narrative;

    JEL classification:

    • B49 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Other
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • N43 - Economic History - - Government, War, Law, International Relations, and Regulation - - - Europe: Pre-1913

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