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We said players should never play a strategy that's never a best response to anything, so we threw those away.
我们学到了参与人不应该选择,非最佳对策的策略,应该剔除它们
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Identify the best responses of each player as a function of the others and find out where they intersect.
把每个人的最佳对策看成别人策略的函数,然后找出函数的交点
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I threw away all strategies that were never a best response, then I looked at the strategies that were left.
我剔除了非最佳对策的策略,然后我看看还剩下哪些策略
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Each of them is trying to play a best response for what they anticipate the other person's going to do.
每家公司都想采取预料的对方策略的,最佳对策来制定产量
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I could do the same thing for Player 2 to find Player 2's best response for every possible choice of Player 1.
同理对于参与人2来说,可以算出参与人1不同策略的最佳对策
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The strategies I'm about to throw away now, they're not--it isn't that they're not best responses, they are best responses to something.
我要剔除的策略,并非都不是最佳对策,它们可能是某种情况下的最佳对策
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Good, so what I have here is an equation that tells me Player 1's best response for each possible choice of Player 2.
这个方程表示,参与人2不同策略下参与人1的最佳对策
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And since that was the best you could do under that belief, you'll hopefully keep your job.
因为那的确是在这种信念下的最佳策略,你也就不会因此被炒鱿鱼了
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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 here is the best response of Firm 1 to each possible choice of Firm 2.
这是公司2每种策略下公司1的最佳对策
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But the things they were best responses to, we know are not going to be played, because they themselves were not best responses to anything.
我们都知道使他们成为最佳对策的策略,是不会有人采用的,因为这些策略本身又不是最佳对策
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Each of these firms, we know the fact that they're playing best response, is maximizing their profits taking as giving what the other firm is doing.
每家公司都会采取最佳策略,来根据对手的行为达到最大化利润
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It was don't ever play a strategy that's not a best response to everything.
不要采用非最佳对策的策略
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So are there strategies here that are never a best response to anything?
这些策略都不会成为最佳对策吗
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So some of the strategies that we didn't throw away were best responses to things, but the things they were best responses to have now been thrown away.
这些没有被剔除的策略,是某种情况下的最佳对策,但剩余的最佳对策现在可能也要被剔除
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I said those strategies that were a best response to things that have now been thrown away, but not best response otherwise, I can throw those away too.
这些策略是已被我们的剔除策略的,最佳对策,但仍不是最佳对策,我就剔除它们
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okay I chose Middle because I believed that the other guy was going to choose Right and Middle was the best thing for me to do against Right."
我选中是因为,我认为另一个人会选右,并且选中是右的最佳策略
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There's a more general lesson here, and the more general lesson is, of course: do not choose a strategy that is never a best response to anything you could believe.
从中可以总结出一个更普遍的规律,这个普遍规律就是,不要选择一个在任何情况下,都不是最佳对策的策略
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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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So let's actually, you might want to be a little bit gentle in your own notebook, but on my board let's get rid of all these strategies that are never a best response.
所以我们干脆点,在笔记本上,你们动作轻点,我直接在划掉这些非最佳对策的策略
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We learned that in this game deleting strategies that are never best response, and then deleting strategies that are never best response to anything that is a best response and so on and so forth, yielded a single strategy for each player.
我们学到了在剔除,非最佳对策的策略后,要再剔除那些在对手最佳对策下,不是最佳对策的策略,以此类推,最后每个参与人都只有一个策略了
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These strategies I'm about to delete, it isn't that they're never best responses, they were best responses to things, but the things they were best responses to, are things that are never going to be played, so they're irrelevant.
我现在剔除掉的策略,他们并非不是最佳对策,他们是某些情况下的最佳对策,但是使他们成为最佳对策的条件,是不会发生的,所以它们就不成立
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Once I deleted all the strategies that were never a best response and just focused on that little box of strategies that survived, the picture looked exactly the same as it did before, albeit it blown up and the numbers changed.
一旦剔除了非最佳对策的策略,仔细研究剩下的策略时,图像还和以前看起来是一样的,尽管坐标改变了,图像放大了
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So the thing that I hope jumps out at you from this picture is no great guesses about figuring out this is a ?, so if the probability that the goalie's going to jump to the right is less than a ?, then the best you can do is represented by this green line, which is shoot to the right.
我希望大家都能从图中看出来,得出这一点的横坐标是?不难,如果门将扑向右路的概率,小于?的时候,此时你的最佳策略用这段绿线表示,即你应该从右路射门
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Conversely, if you think the goalie's going to shoot to the right with probability more than a ?, then the best you can do is represented by the pink line, and that's shooting to the left, or if you think the goalie's going to dive to the right with the probability more than a ?, the best you can do, your best response is to shoot to the left.
相反如果你认为门将扑向右侧的概率,大于?的情况下,此时你最佳策略用粉线表示,即从左路射门,也就是说如果你觉得门将扑向右路的,概率大于?的话,你最好选择从左路射门
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So if we know people are not going to play a best response that's never a best response, and we know if we people are not going to play something which is never a best response, and we know people are not going to play which is not a best response, which is not a best etc., etc., etc.
如果我们知道人们不会采用最佳对策,说错了,是不会采用非最佳对策,如果我们知道人们不会采用,非最佳对策的策略,就知道人们不会采用非最佳对策的策略,以此类推了
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So, in particular, I want to figure out what is Player I's best response to each possible choice of Player II?
下面,我想知道怎样计算,参与人I,在参与人II每个策略下的最佳对策呢
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What will Player II's best response look like as a function of Player I's choice in the same picture?
在同一个图像里面怎么表示,参与人II的最佳对策是I策略的函数
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So the line I've just drawn is the best response for Player I as it depends on Player II's choice.
我画的这条线表明参与人I的最佳对策,取决于参与人II的策略
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So the strategies below 1 and above 2 are never a best response for Player I.
也就是说小于1及大于2的策略,都不是参与人I的最佳对策
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