Long before game theory had come along to show analysts how to think about this sort of problem systematically, it had occurred to some actual military leaders and influenced their strategies.

Thus the Spanish conqueror Cortez, when landing in Mexico with a small force who had good reason to fear their capacity to repel attack from the far more numerous Aztecs, removed the risk that his troops might think their way into a retreat by burning the ships on which they had landed.

The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern (1944).

And the greater the soldiers' belief that the battle will be won, without the need of any particular individual's contributions, the less reason they have to stay and fight.

If each soldier this sort of reasoning on the part of the others, all will quickly reason themselves into a panic, and their horrified commander will have a rout on his hands before the enemy has fired a shot.

It may occur to him that if the defense is likely to be successful, then it isn't very probable that his own personal contribution will be essential.

But if he stays, he runs the risk of being killed or wounded—apparently for no point.

It cannot be wise to attack an opponent who has a good reason (whatever, exactly, it might be) for being sure that he can't lose.

The Aztecs therefore retreated into the surrounding hills, and Cortez had his victory bloodlessly.

(Most armies try to avoid this problem just as Cortez did.

Since they can't usually make retreat impossible: they shoot deserters.

Thus we could imagine, without contradiction, a circumstance in which an army, all of whose members are brave, flees at top speed before the enemy makes a move.

If the soldiers really of many individually rational decision-making processes—one process per soldier—produces an outcome intended by no one.

This situation has dramatically changed, in ways we will examine as we go along, over the past six decades, as the framework has been deepened and generalized.