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

Mongin, Philippe (2017): A Game-Theoretic Analysis of the Waterloo Campaign and Some Comments on the Analytic Narrative Project. Forthcoming in: Forthcoming in Cliometrica , Vol. 11, (2018)

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Keywords: Napoléon, Waterloo, military history, rational choice theories, game theory, zero-sum two-person games, analytical narrative
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B4 - Economic Methodology > B49 - Other; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; N - Economic History > N4 - Government, War, Law, International Relations, and Regulation > N43 - Europe: Pre-1913

References

Allison, G.T. (1971), Essence of Decision: Explaining the Cuban Missile Crisis, 1ed. Little Brown (2ed. coauthored with P. Zelikow, Longman, 1999).

Aron, R. (1976), Penser la guerre, Paris, Editions Gallimard, 2 t. Eng. transl. by C. Booker and N. Stone, Clausewitz : Philosophy of War, Englewood Cliffs, NJ, Prentice-Hall, 1985.

Barthes, R. (1966), "Introduction à l'analyse structural des récits", Communications, 8, p. 1-27. Engl. version as "An Introduction to the Structural Analysis of Narrative", New Literary History, 6, p. 237-272.

Bassford, C. (1994), Clausewitz in English : The Reception of Clausewitz in Britain and America, 1815-1945, New York, Oxford University Press.

Bates, R.H., A. Greif, M. Levi, J.L. Rosenthal, B. Weingast (1998), Analytic Narratives, Princeton, Princeton University Press.

Bates, R.H., A. Greif, M. Levi, J.L. Rosenthal, B. Weingast (2000), "The Analytic Narrative Project", American Political Science Review, 94, p. 696-702.

Bertrand, H.G. (undated), Cahiers de Sainte-Hélène, ed. by P. Fleuriot de Langle, Paris, Albin Michel, 1949-1959, 3 vol.

Brams, S. (1975), Game Theory and Politics, New York, Free Press.

Brams, S. (2011), Game Theory and the Humanities: Bridging Two Worlds, Cambridge, MA, MIT Press.

Browning, B.M. (2000), "Economic Analysis in Historical Perspective", History and Theory, 39, p. 88-97.

Clausewitz, C. von (1832-1837), Hinterlassene Werke, 10 vol., Berlin, F. Dümmler (posthumous edition by Marie von Clausewitz).

Clausewitz, C. von (1832-1834), Vom Kriege, in Hinterlassene Werke, vol. 1-3. New ed. by W. Hahlweg, Bonn, Dümmler, 1980. Eng. ed. and trans. by M. Howard and P. Paret, On War, New York, Everyman's Library, 1993.

Clausewitz, C. von (1835), Der Feldzug von 1815 in Frankreich, in Hinterlassene Werke, vol. 8, or in Schriften, Aufsätze, Studien, Briefe, ed. by W. Hahlweg, Göttingen, Vandenhoeck & Ruprecht, 1990, 2 vol., p. 936-1118. Eng. trans. in C. Bassford (ed.), On Waterloo : The Campaign of 1815 in France by Carl von Clausewitz and a Memorandum on the Battle of Waterloo by the Duke of Wellington, Boulder, Co., Westview Press, 2001. French tr. by M. Niessel, La campagne de 1815 en France, Paris, R. Chapelot, 1900. Reprint Paris, Champ Libre, 1973.

Davidson, D. (1980), Essays on Actions and Events, Oxford, Clarendon Press.

Davidson, D. (2004), Problems of Rationality, Oxford, Clarendon Press.

Earle, E.M. (1943) (ed.), Makers of Modern Strategy, Princeton, Princeton University Press.

Elster, J. (2000), "Rational Choice History: A Case of Excessive Ambition", American Political Science Review, 94, p. 685-695.

Fuller, J.C. (1951-1956), The Decisive Battles of the Western World and their Influence upon History, London, Eyre & Spottiswoode.

Gourgaud, G. (1818), Campagne de 1815, Paris, P. Mongie Aîné.

Grenier, J.Y., C. Grignon, P.M. Menger (2001) (eds) Le modèle et le récit, Paris, Editions de la Maison des sciences de l'homme.

Grouchy, E. de (1873-1874), Mémoires du Maréchal de Grouchy. Publié par le Marquis de Grouchy, Paris, E. Dentu, 1873-1874.

Haywood Jr., O.G. (1950), "Military Decision and the Mathematical Theory of Games", Air University Quarterly Review, 4, p. 17-30.

Haywood Jr., O.G. (1954), "Military Decision and Game Theory", Journal of the Operations Research Society of America, 2, p. 365-385.

Herbert-Rothe, A. (2005), "Clausewitz und Napoleon: Jena, Moskau, Waterloo", in Clausewitz-Gespräch vom 1. Dezember 2005, ed. by L. Souchon, Hamburg, Internationales Clausewitz-Zentrum, Führungsakademie der Bundeswehr.

Hofschröer, P. (1998-1999), The Waterloo Campaign, Londres, Greenhill Books, 2 vol.

Houssaye, H. (1905-1906), 1815, 3 vol., Paris, Perrin et Compagnie. Reprint of vol. 2, Waterloo, Paris, Librairie académique Perrin, 1961.

Largeaud, J.M. (2006), Napoléon et Waterloo: la défaite glorieuse de 1815 à nos jours, Paris, La Boutique de l'Histoire.

Las Cases, E. de (1823), Le Mémorial de Sainte-Hélène. Reprint Paris, Garnier, 2 t., 1961. Eng. trans. Memoirs of the Life, Exile and Conversations of the Emperor Napoleon by the Count of Las Cases, New York, W.J. Widdleton, 1879, 4 vol.

Leonard, R. (2010), Von Neumann, Morgenstern and the Creation of Game Theory: from Chess to Social Science, New York, Cambridge University Press.

Levi, M. (2002), "Modeling Complex Historical Processes with Analytic Narratives", in R. Mayntz, Akteure-Mechanismen-Modelle, Campus, Schriften des Max-Planck-Institute für Gesellschatsforschung Köln, 42, p. 108-127.

Levi, M. (2004), "An Analytic Narrative Approach to Puzzles and Problems", in I. Shapiro, R. Smith and T. Masoud (eds), Problems and Methods in the Study of Politics, p. 201-226. New York, Cambridge University Press.

Luce, R.D and H. Raiffa (1957), Games and Decisions, New York, Wiley.

Mauduit, H. de (1847), Histoire des derniers jours de la Grande Armée. Reprint Paris, L.C.V. Services, Collection Mémoires d'Empire, 2006.

Meade, E.M. (1943), Makers of Modern Strategy, Princeton University Press.

Mongin, P. (2006), "Value Judgements and Value Neutrality in Economics", Economica, 73, p. 257-286.

Mongin, P. (2009), "Waterloo et les regards croisés de l’interprétation", in A. Berthoz (ed.), La pluralité interprétative, Paris, Odile Jacob.

Mongin, P. (2010), "Analytic Narrative", in J.E. Alt, S. Chambers, G. Garrett, M. Levi, P. McClain (eds), The Encyclopedia of Political Science, 1, p. 48-51.

Mongin, P. (2011), "La théorie de la décision et la psychologie du sens commun", Information sur les sciences sociales/Social science Information, 50, p. 351-374. (English translation available on request.)

Nash, J.F. (1950), "Equilibrium Points in n-Person Games", Proceedings of the National Academy of Sciences, 36, p. 286-162.

von Neumann, J. (1928), "Zur Theorie der Gesellschaftsspiele", Mathematische Annalen, 100, p. 295-320.

von Neumann, J. et O. Morgenstern (1944), Theory of Games and Economic Behavior, New York, Wiley (2nd rev. ed., 1947).

North, D.C. (1990), Institutions, Institutional Change, and Economic Performance, Cambridge, Cambridge University Press.

O'Neill, B. (1994), "Game Theory Models of Peace and War", ch. 29 in R.J. Aumann and S. Hart (eds), Handbook of Game Theory with Economic Applications, vol. 2, Amsterdam, Elsevier.

Paret, P. (1992), Understanding War. Essays on Clausewitz and the History of Military Power, Princeton, Princeton University Press.

Pareto, V. (1917-1919), Traité de sociologie générale. Reprinted as vol. XII in Œuvres complètes, Genève, Droz, 1968. Eng. trans. by A. Bongiorno and A. Livingston, The Mind and Society: a Treatise on General Sociology, Dover, New York, 19363.

Popper, K. (1967), "La rationalité et le statut du principe de rationalité", in E.M. Claassen (ed.), Les fondements philosophiques des systèmes économiques, Paris, Payot, p.142-150. Eng. version "The Rationality Principle", in D. Miller (ed.), Popper Selections, Princeton, Princeton University Press, 1982, p. 357-365.

Roberts, A. (2005), Waterloo, London, HarperCollins.

Schelling, T. (1960), The Strategy of Conflict, Cambridge, Mass., Harvard University Press.

Weber, M. (1922a), Wirtschaft und Gesellschaft, Tübingen, Mohr et Siebeck. Eng. trans. by G. Roth, C. Wittich, E. Fischoff, Economy and Society: An Outline of Interpretive Sociology, University of California Press, 1978.

Weber, M. (1922b), Gesammelte Aufsätze zur Wissenschaftslehre, Tübingen, Mohr et Siebeck. Partial Eng. trans. by E. A. Shils and H. A. Finch, The Methodology of the Social Sciences, New York, Free Press, 1949.

Zagare, F.C. (2009), "Explaining the 1914 in Europe. An Analytic Narrative", Journal of Theoretical Politics, 21, p. 63-95.

Zagare, F.C. (2011), The Games of July: Explaining the Great War, Ann Arbor, University of Michigan Press.

Zagare, F.C. (2015), "The Moroccan Crisis of 1905-1906: An Analytic Narrative", Peace Economics, Peace Science and Public Policy, 21, p. 327-350.