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For reasons to be discussed later, limitations in their mathematical framework initially made the theory applicable only under special and limited conditions.
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.
Refinements are still being made, and we will review a few outstanding problems that lie along the advancing front edge of these developments towards the end of the article. Despite the fact that game theory has been rendered mathematically and logically systematic only sincegame-theoretic insights can be found among commentators going back to ancient times.
Consider a soldier at the front, waiting with his comrades to repulse an enemy attack. 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, 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? 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 fired a shot.
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.
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.
He took care to burn his ships very visibly, so that the Aztecs would be sure to see what he had done. They then reasoned as follows: Any commander who could be so confident as to willfully destroy his own option to be prudent if the battle went badly for him must have good reasons for such extreme optimism.
The Aztecs therefore retreated into the surrounding hills, and Cortez had his victory bloodlessly. These two situations, at Delium and as manipulated by Cortez, have a common and interesting underlying logic.
Notice that the soldiers are not motivated to retreat just, or even mainly, by their rational assessment of the dangers of battle and by their self-interest. Rather, they discover a sound reason to run away by realizing that what it makes sense for them to do depends on what it will make sense for others to do, and that all of the others can notice this too.
Even a quite brave soldier may prefer to run rather than heroically, but pointlessly, die trying to stem the oncoming tide all by himself.Yahoo Lifestyle is your source for style, beauty, and wellness, including health, inspiring stories, and the latest fashion trends.
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