The hay, that is, well, what? The payoff, what the poem is all about, what mowing is all about.

这堆草又是什么呢，是成果，诗歌的成果，割草的结果。

耶鲁公开课 - 现代诗歌课程节选

The payoff of 2 against 3 is all the people at 1, all the people at 2, so it's 20%.

如果对手选3而我选2我会得到,立场1和2的全部选票,一共20%

耶鲁公开课 - 博弈论课程节选

But the point is that this form of immortality is available to Tellus because of his place in the polis, because of the deeds he does for the polis, and that is the greatest possible payoff.

但是关键是,特勒斯之所以能成为永恒,是因为他在城邦中的地位,是因为他在城邦之中的功绩,这也许就是得以永存的最佳途径

耶鲁公开课 - 古希腊历史简介课程节选

So I shoot to the left and the goalie dives to the left, my payoff is what? It's 4.

我从左路射门而门将也扑向左路时,我的收益是4

耶鲁公开课 - 博弈论课程节选

Then we're going to compare my payoff from choosing 1 against the other candidate's payoff from choosing 1.

我们来计算当对手选立场1时,我也选立场1获得的收益

耶鲁公开课 - 博弈论课程节选

So his payoff, the attacker's payoff, is how many battalions does he get to bring into your country?

入侵者的收益,是他攻入你国家时还剩余多少兵力

耶鲁公开课 - 博弈论课程节选

We need to give a little bit more structure on the payoff before I get to the payoffs.

在告诉大家收益之前,还需要知道一些别的东西

耶鲁公开课 - 博弈论课程节选

If I shoot to the left and the goalie dived to the right, then I score 90% of the time, so my payoff is .9.

如果我从左路射门而门将扑向右路,那我有90%的概率进球,即我的收益就是9

耶鲁公开课 - 博弈论课程节选

So what's my payoff if I choose 1 and my opponent chooses 2?

我选立场1对手选立场2我收益是什么

耶鲁公开课 - 博弈论课程节选

We mean that if these are your payoffs, no matter what your pair does, you attain a higher payoff from choosing Alpha, than you do from choosing Beta.

我们说如果这是你的收益,那么不论你的对手选什么,你选择α总会比选择β,得到更好的收益

耶鲁公开课 - 博弈论课程节选

Let's start by plotting my expected payoff from choosing the strategy Up.

我先把选上的预期收益,标注出来

耶鲁公开课 - 博弈论课程节选

What about my expected payoff from choosing Middle against , so in this case where I think it's equally likely that my opponents going to choose Left or Right?

那我在情况下,选中的预期收益是什么呢,在此情况下我依然认为,对手选左选右的可能性相同

耶鲁公开课 - 博弈论课程节选

And here's my green line representing my expected payoff as the shooter, from shooting to the right, as a function of the probability that the goalie dives to the right.

这条绿线表示作为一个罚球球员,我从右路射门的收益,是门将扑向右路概率的一个函数

耶鲁公开课 - 博弈论课程节选

How about my expected payoff from choosing Down versus ?

那在情况下我选下的预期收益呢

耶鲁公开课 - 博弈论课程节选

So the payoff from choosing 2 against 2 is 50%.

如果双方都选立场2则各得50%选票

耶鲁公开课 - 博弈论课程节选

So how about my payoff versus 1, for example.

如果对手选立场1我收益如何

耶鲁公开课 - 博弈论课程节选

So what we're going to look at is the expected payoff of Up versus, let me call it a : a being equally likely that my opponent chooses Left and Right.

所以接下来我们看看在我认为对手,选择左右的可能性相同下的预期收益,我们把它称为

耶鲁公开课 - 博弈论课程节选

What's the payoff from choosing 3 against 2?

我选立场3对手选立场2的收益是什么

耶鲁公开课 - 博弈论课程节选

Probability is 0 of their choosing Right is the same as saying they choose Left, so that my payoff from Up against that is given by the top box up there, I get 5.

如果对手选右的概率是0,其实就是说他们会选左,因此此情况下我选上的收益,从上面的矩阵看,我的收益是5

耶鲁公开课 - 博弈论课程节选

I took the second payoff from that matrix and made it the second payoff in this matrix.

那个矩阵里面的第二个收益就是,这次博弈的矩阵里第二个收益

耶鲁公开课 - 博弈论课程节选

Once again the row player is the first payoff and the column player is the other payoff.

这次还是第一个收益是我的,另一个收益是我对手的

耶鲁公开课 - 博弈论课程节选

We're going to compare this with my payoff from choosing 2 against the other candidate choosing 1.

我们再计算当对手选择立场1时,我选择立场2获得的收益

耶鲁公开课 - 博弈论课程节选

So in this case, my expected payoff is a ? of 1 plus a ? of 4, for a total of again 2.5.

在这种情况下,我预期收益是?乘1加?乘4,总和还是2.5

耶鲁公开课 - 博弈论课程节选

So you might think that maybe middle dominates left, but notice that middle has a higher payoff against left than shooting to the left.

你可能认为中路比左路好,那请你仔细看一下在门将扑向左路时,从中路射门的收益确实比左路高

耶鲁公开课 - 博弈论课程节选

So what's my expected payoff from choosing Up where I believe the other person's going to choose Left and Right, equally likely? It's what?

那么在我对手选择左或右,可能性相同的情况下,我的预期收益会是什么样的呢

耶鲁公开课 - 博弈论课程节选

So in both cases, no matter what the other person does, she receives a higher payoff from choosing Alpha, so she should choose Alpha.

这两种情况下,无论别人怎么选,她选α总能得到更好的成绩,所以她应该选α

耶鲁公开课 - 博弈论课程节选

So this point here corresponds to my payoff if I choose Up and they choose Right.

也就是说这个点表示,我选上对手选右时我的收益

耶鲁公开课 - 博弈论课程节选

And the second payoff is the column player's payoff, in this case the indignant angel.

第二个收益的是,愤怒天使的收益

耶鲁公开课 - 博弈论课程节选

So this line represents the expected payoff of shooting to the middle as a function of the probability that the goal keeper dives to the right.

这条线表示从中路射门时罚球者的收益,是门将扑向右路概率的一个函数

耶鲁公开课 - 博弈论课程节选

So now we're comparing my choosing 1, when my opponent chooses 2, and the payoff I would get if I choose 2 when my opponent chooses 2.

当我选择立场1,而对手选择立场2时,或者如果我们都选择立场2,我的收益会是怎么样的

耶鲁公开课 - 博弈论课程节选