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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

And success, as a fourteen years-old squash player, was the most important thing in my life.

成功对14岁的壁球手来说，是我生命中最重要的东西。

哈佛公开课 - 幸福课课程节选

Treat the computer as though it were just a great chess player.

将计算机视为一名象棋健将

耶鲁公开课 - 死亡课程节选

Because at this point, as in the partnership game, which there was a similar thing, as in the partnership game where the best responses intersect is where Player 1 is playing a best response to Player 2, and Player 2 is playing a best response to Player 1.

因为这一点,与合伙人博弈的情况一样,两者的情况是很类似的,合伙人博弈中最佳对策曲线的交点处,参与人1采用了回应参与人2的最佳对策,参与人2采用了回应参与人1的最佳对策

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 here's Player I's payoff as a function of what Player II chooses and what Player I chooses, so we have that already.

这个就是参与人I的收益的方程,它是参与人I和II策略的函数,我们已经得到了

耶鲁公开课 - 博弈论课程节选

So at this point I've found player 1's best response as a function of q2.

就能得出参与人1最佳对策是q2的函数

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

So the best response for Player 1, as a function of what Player 2 chooses, q2, is just equal to the q1 hat in this expression and if I solve that out carefully, I will no doubt make a mistake, but let's try it.

这个就是参与人1的最佳对策,它是参与人2策略q2的一个函数,它和之前的q1帽那个表达式是相等的,虽然我是很仔细地计算的,还是有可能算错的,我来验证一下

耶鲁公开课 - 博弈论课程节选

So the expression I wanna draw first of all is the best response of Player I as a function of S2 and we agreed that that was given by 1 plus 1/4 now, 1 plus 1/4 S2.

首先我们想要绘制的表达式是,参与人I的最佳对策是S2的函数,我们都知道它等于1+S2/4

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

I've found Player 2's best response as a function of q1, and the way I did it, just remember, the way I did was I applied a little bit of 112 and high school calculus, so that's your single variable calculus.

以及参与人2的最佳对策是q1的函数,而且我们用到的数学知识,只是稍微与112和高中微积分有关,仅仅是单变量微积分的知识

耶鲁公开课 - 博弈论课程节选