Friday, August 01, 2014

Corterz and game theory

Cortez was good at game theory. So I was reading up on some game theory recently and came across an article in the Stanford Encyclopedia of Philosophy called Game theory. The opening is awesome as there was this,
Consider a soldier at the front, waiting with his comrades to repulse an enemy attack. 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. On the other hand, if the enemy is going to win the battle, then his chances of death or injury are higher still, and now quite clearly to no point, since the line will be overwhelmed anyway. Based on this reasoning, it would appear that the soldier is better off running away regardless of who is going to win the battle. Of course, if all of the soldiers reason this way—as they all apparently should, since they're all in identical situations—then this will certainly bring about the outcome in which the battle is lost. Of course, this point, since it has occurred to us as analysts, can occur to the soldiers too. Does this give them a reason for staying at their posts? Just the contrary: the greater the soldiers' fear that the battle will be lost, the greater their incentive to get themselves out of harm's way. 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 anticipates 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 even fired a shot.
So before even finishing the paragraph it occurred to me that commanders had, at times to counter this. I can not recall the situation but I remember reading about a Chinese general placing his highly outnumbered army by a river when facing the enemy so they could not retreat. The option was simply removed. Then I read on and this,
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. With retreat having thus been rendered physically impossible, the Spanish soldiers had no better course of action but to stand and fight—and, furthermore, to fight with as much determination as they could muster.
I had forgotten about that. I am guessing that was a far more common tactic than I am aware of.

And speaking of famous no retreat moments….


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