The Battles of Waterloo

It is the 200th anniversary of the Battle of Waterloo on 18 June. The Bicentenary is being celebrated with 5000 re-enactors, 300 horses and 100 canons.

News of the celebrations has taken me back to Philippe Mongin’s 2009 paper, A Game-Theoretic Analysis of the Waterloo Campaign and Some Comments on the Analytic Narrative Project.

In his paper Phillippe presents a game-theoretic model of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. Phillippe looks in particular at 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”.

On page 7 of the paper he proposes a model for:

Napoleon’s all-crucial decision, June 17, 1815, the day after his victory over Blucher at Ligny. That day he chose to send more than a third of his forces, under the command of Grouchy, against the retreating Prussians. All the commentators agree that this division of the French army was the key to Wellington’s victory, June 18 at Waterloo. Grouchy spent the fateful day at Wavre, baited by Blucher’s rear guard, while the advance guard marched unimpeded to join Wellington in the mist of an uncertain battle. The campaign’s greatest question, which involves Napoleon’s rationality, is whether he could have made better use of Grouchy’s detachment. The model we propose to answer this question takes the form of a simple zero-sum game between Napoleon and Blucher. Despite the absence of Grouchy as an autonomous player, it adds precision to the competing hypotheses.


Section 3 of Phillippe’s paper provides extensive detail to support the game theoretic approach. As I worked my way through his model, I was fascinated by the interplay of other observations on events … and the opportunities for an integration of historical narrative and rational choice modeling.

I do think there are some fascinating opportunities here for observing and analysing sport performance. A 2013 paper by Hayrettin Altinbay offers some additional insights into how this integration might occur.

Perhaps we could start with an iconic moment from Rugby. Could the New Zealand All Blacks have prevented this 1973 try?

Photo Credits

Waterloo, Belgium (cjlvp, CC BY-NC-ND 2.0)

Battlefield at Waterloo (Eric Wilcox, CC BY-NC 2.0)

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