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 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 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

It's the expected payoff to Player 1 if shooting to the left as it depends on the probability that the goal keeper dives to the right.

它表示参与人1,从左路射门的预期收益,与门将扑向右路的概率有关

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 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

So very similar idea, but the only thing is, I'm slightly abusing notation here by saying that my payoff depends on my strategy and a belief, but what I really mean is my expected payoff.

这和以前的概念差不多,唯一的不同,就是我这里稍微用了一些数学符号,来表述策略带来的收益与所持信念有关,这里的收益指的是预期收益

耶鲁公开课 - 博弈论课程节选

What do I mean by expected payoff?

预期收益是什么意思呢

耶鲁公开课 - 博弈论课程节选

And we already know if I look at the probability of a ?, which is here, that the payoff I get from choosing, the expected payoff I get from choosing up against a is 2.5.

我们已经计算过了概率是?的情况,即在对手概率是的情况下,我选择上我从中获得的,预期收益是2.5

耶鲁公开课 - 博弈论课程节选

It maximizes my expected payoff.

它最大化了我的预期收益

耶鲁公开课 - 博弈论课程节选

What I suggest we do is we do what we did last time and we start to draw a picture to figure out what my expected payoff is, depending on what I believe the goalie is going to do.

我建议用上次的方法,作图来表示在我对门将的策略,存在某种信念下,我的预期收益

耶鲁公开课 - 博弈论课程节选

So here's the straight line, and this line is the expected payoff to Player I from choosing Down as it depends on the probability that the other person chooses Right, and then once again, we can write down the equation.

这就是第三条直线了,它表示参与人I选择下获得的收益,是另一个参与人,选右概率的一个函数,对于这一条直线,我们依然能够给出方程式

耶鲁公开课 - 博弈论课程节选

This is the payoff to Player I of choosing Middle against Right, and the line in between, this line here, is the expected payoff to Player I of choosing Middle as a function of the probability that other people choose Right.

这条表示对手选右时参与人选中的收益,两个端点中间的线段部分,表示参与人I选右的预期收益,它是对手选右概率的一个方程

耶鲁公开课 - 博弈论课程节选