All of you chose Down, but Up does best against Left and Middle does best against Right.
你们都选择下,可是选上是左的最佳对策,而选中是右的最佳对策
So last time we introduced a new idea and the new idea was that of best response.
上一讲我们引入了一个新概念,这个新概念就是最佳对策
And to what extent are they best explained in terms of an interaction?
在多大的程度上这些区别,可以从相互作用的角度得到最佳的解释
The citizen of the best regime he says must be able to sustain war if duty requires but only for the sake of peace and leisure.
最佳政体的公民,据他所说,如果有义务上的需要,必需要能承担战争,但目的必需仅限于为了和平与安逸。
It turns out that one of the places that's been very fruitful to look for proteins that differ between cell populations is on the surface of the cell.
而事实证明,寻找能鉴别细胞种类的,特定蛋白的最佳位置,是在富含蛋白的细胞膜上
When the stock market is going up they think that -they increasingly think that the stock market is just the best investment, until when it starts falling, then they start retracting from that.
当股票市场上行时,越来越多的人会觉得,股票是最佳投资选择,而当股市下跌时,人们纷纷从股市中撤出
So if you've got putty or terminal up on the screen, -- and you're having some trouble that's really best seen with -- in that natural environment, we can actually see sort of tech-support style on the right-hand side what you're doing, and you can see everything we're doing.
所以如果你有Putty软件或者终端机在屏幕上,你遇到一些麻烦来显示最佳状态-,在那个自然环境中,我们可以看到很多,技术支持类型,在你们做的东西的右手边,你们可以看我我们在做的一切。
So we found precisely one point on this best response picture, and there's a lot of points to find, and it's 20 past 12, so we better get going.
现在我们只找到了最佳对策曲线上的一点,我们还需要找到更多的点,现在12点20了,我们得快点了
We know that Up does best against Left.
我们知道上是左的最佳对策
So Up, as I say, does best against left.
选上是对手选左时的最佳对策
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
Everyone agree because 5 is bigger than 1, and 5 is bigger than 4, so Up is and to use a technical term we'll define formally next time Up is the best response to Left.
大家都知道5大于1,5也大于4,所以选上是,以后我们就要用术语来说了,选上是左的最佳对策
I'm going to put down two different definitions of best response, one of which corresponds to best response to somebody else playing a particular strategy like left and right, and the other is just going to correspond to the more general idea of a best response to a belief.
我写出最佳对策的两种不同形式定义,一个是参与人针对对手策略的定义,比如这里的左路右路,另一个强调的是,最佳对策的广义上的定义
To make this a first order condition, I'm going to say "at the best response," put a hat over the 1.
为了达到一阶条件,我说在最佳对策下,在S1上写个帽
If I think the probability that they're going to choose Right is less than X, then my best response is to choose Up.
也就是说如果我觉得,对手选右的概率小于X,那我的最佳对策是选上
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