alpha~ Says:
04月 25th, 2009 at 3:34 pm Vote: 0 0
看见有人的质疑：

『de-sci.org 博弈论小史Posted by 传播数学 is wrong!
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送交者: 短江学者 于 2009-04-24, 22:13:26:

传播数学says:

引用：
而 Minmax 定理, 就是说, 二人零和博弈问题, 一定存在一个解, 这个解对于两个人来说, 都是最佳的策略.

This is wrong. John von Neumann’s contribution is to introduce the mixed strategies so that a zero sum game would always have a solution. With only pure strategies a zero sum game often does not have a solution. See, for example, wiki:

引用：
The minimax theorem states:

For every two-person, zero-sum game with finite strategies, there exists a value V and a mixed strategy for each player, such that (a) Given player 2’s strategy, the best payoff possible for player 1 is V, and (b) Given player 1’s strategy, the best payoff possible for player 2 is -V.

and

引用：
A mixed strategy is an assignment of a probability to each pure strategy. This allows for a player to randomly select a pure strategy. Since probabilities are continuous, there are infinitely many mixed strategies available to a player, even if their strategy set is finite.