We're going to assume that everybody knows the possible strategies everyone else could choose and everyone knows everyone else's payoffs.

我们假设,每个人都知道其他人可能选择的策略,每个人都知道其他人的收益

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Delete those. Delete those for everyone else, because everyone else is not going to play a dominated strategy.

应该剔除它们,其他人也会这么做,因为其他人也不会,采用劣势策略

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The more I did of my strategy, the more the other player did as a best response.

我如果采用付出更多努力的策略,其他参与人的最佳对策也是这样

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So in previous definitions, we've seen the qualifier, for all, be on the other player's strategy.

在以前的定义中,“对所有的”这个限定词,修饰的是其他参与人的策略

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The idea was to think of a strategy that is the best you can do, given your belief about what the other people are doing: what your opponents are doing, what other players are doing.

在你已经对别人如何行动有一定信念时,你能想到的最佳的策略,你的对手会怎么做,其他人又会怎么做

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Is anything else dominated here?

还有其他的劣势策略吗

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So this is a choice for all except person "i" or Player i.

它表示除i外其他参与人每人的策略

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So strategy ?i is a best response to the strategy S-i of the other players if my payoff from choosing ?i against S-i, is weakly bigger than that from choosing Si' against S- i, and this better hold for all possible other strategies I could choose.

策略?i是其他参与人策略S-i的,最佳对策,如果此时我选?i的收益,弱优于此情况下选Si'的收益,这对于所有我可以选择的策略都成立

耶鲁公开课 - 博弈论课程节选