Three years later, Meryl Streep won Best Actress for her work in the movie "Sophie's Choice."

VOA: special.2009.05.29

We could choose any two quantities, and, in fact, it turns out that these are going to prove, after we have the second law, not to be the best choice.

我们可以任选两个物理量，其实，在学习了热力学第二定律之后，我们可以证明，这样的选择并不是最好的。

麻省理工公开课 - 热力学与动力学课程节选

What Thomas said was, right is never a best choice, that's true.

托马斯所说右并非总是,最优策略,这是对的

耶鲁公开课 - 博弈论课程节选

But yeah, right is never the best choice.

但是右绝不是最优策略

耶鲁公开课 - 博弈论课程节选

So it turns out that, as the gentleman out there said, if I thought it was equally likely that my opponent was going to choose Left or Right, then actually my best choice, my best response is to choose Down.

这个结果和刚才那位先生说的,如果我觉得我对手,选择左或右的可能性相同的话,这时候最好的选择,也就是说我的最佳对策是选下

耶鲁公开课 - 博弈论课程节选

But we also saw it's a dangerous idea to take too literally: that sometimes this can get you to over think the problem and actually, as in that numbers game last time, the best choice, the winning choice, might not involve so many rounds.

同时我们也发现过度照本宣科也不好,有时他会导致你,对于问题的过度探究,正如我们上次玩的数字游戏,最优选择,最后获胜的答案,有时不会绕那么多弯子

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

So what we're going to do is we're going to figure out Player 1's best response quantity to each possible choice of Player 2, and then we're going to flip it around and figure out Player 2's best response quantity to each possible choice of Player 1, and then we're going to see where those coincide, where they cross.

下面我们就需要表示出,参与人1对于2不同产量下的最佳产量,然后反过来写出,在参与人1的不同产量下,参与人2的最佳产量,然后再来看看这两者在哪里相交

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

So for each possible choice of S2, I'm going to draw Player I's best response and we'll do it in red.

对于任意定义域内的S2,我用红色来表示参与人I的最佳对策

耶鲁公开课 - 博弈论课程节选

What is Player I's best response for each possible choice S2 of Player II?

每个s2下参与人I的最佳对策是什么

耶鲁公开课 - 博弈论课程节选

So what I need to do then is I need to figure out what is Player 1's best response for each possible choice q2 of Player 2.

所以我们要先找出,在参与人2的每个可选策略q2下,参与人1的最佳产量

耶鲁公开课 - 博弈论课程节选

We have Player I's payoff as a function of the two efforts and now I want to find out what is Player I's best efforts given a particular choice of S2? Yeah.

参与人I的收益是两人付出的函数,那么对于某个给定的S2,怎么计算参与人I的最佳对策呢

耶鲁公开课 - 博弈论课程节选

I found out what Player I's best response was for every possible choice of Player II, and I found out what Player II's best response was for every possible strategy of Player I.

我发现了参与人I的最佳对策,取决于参与人II的可选策略,同时也发现,参与人II的最佳对策,取决于参与人I的可选策略

耶鲁公开课 - 博弈论课程节选

I know that Player 2's best response for every possible choice of Player 1, which if we had done it would be q2 hat is going to a -c over 2b--q1 over 2, right?

参与人1不同策略下参与人2的最佳对策,即q2帽等于/2b - q1/2

耶鲁公开课 - 博弈论课程节选

So similarly, I would find that ?2 2 equals 1 plus B S1 and this is the best response of Player II, as it depends on Player I's choice of effort S1.

同理可得?2等于1+B*S1,?2是参与人II的最佳对策,因为它与参与人I的策略S1有关

耶鲁公开课 - 博弈论课程节选

Okay, now I found out what PlayerIi's best response is to Player II, and what Player II's best response is to Player I for each possible choice of Player II up here, and for each possible choice of Player I down there.

好了,我们已经找到了参与人I,和参与人II互相的最佳对策了,这些是在参与人II有上面的可能策略,同时参与人I有下面的可能策略情况下

耶鲁公开课 - 博弈论课程节选

So this the best response for Player II for every possible choice of Player I, and just to make sure we understand it, what this blue line tells me is you give me an S1, an effort level of Player I, I read up to the blue line and go across and that tells me Player II's best response.

这就是在任意参与人I的可选策略下,参与人II的最佳对策,为了让大家都明白,这条蓝色线表示给定一个S1,即参与人I的付出,通过查找蓝色的线,可以得出参与人II的最佳对策

耶鲁公开课 - 博弈论课程节选