Colonel Blotto Divides His Army
Two colonels must each secretly split a fixed number of troops across several battlefields, deciding all at once with no knowledge of the other's plan. Whoever puts more troops on a given battlefield wins it outright, and whoever wins the most battlefields wins the war. Is there one 'best' way to divide your troops that beats every possible strategy your rival might choose?
Reveal the answer
No — there's no single dominant allocation. Any fixed split can be beaten by a rival who concentrates slightly more strength wherever you're thin, so the only equilibrium involves randomizing your allocation. Formulated by French mathematician Émile Borel in 1921 as an early model of competitive resource allocation, 'Colonel Blotto' games are now used to study election spending, advertising wars, and network defense.