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In these "games of strategy," to use a modern term, if one party chooses a strategy, then this strategy will form part of the data which the other party should consider in choosing his own strategy. This is obviously true if each party announces his strategy, but it is also true if each party tries to conceal his strategy. In the latter case each will try to guess the other\'s strategy, while choosing a strategy for himself which will not be anticipated by his opponent. In each case an individual\'s choice of strategy depends on his opponent\'s choice or on his estimate of his opponent\'s choice. Examining the games with which they were familiar, the mathematicians discovered that any effort to specify the "correct" rules for a player wishing to win as much as possible led to an infinite regress. If the proper strategy for player A was strategy 1, then player B should take that fact into account and choose strategy 2, but if B chose strategy 2, then 1 was not the proper strategy for A, who should choose 3, etc. These early investigators, therefore, concluded that this type of problem was insoluble and confined their investigations to pure games of chance.

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