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

And there are different choices here 1, 2, 3, and 4 for Player I, and here's the 45o line.

参与人I有1一直到4的可选策略,这条是45°线

耶鲁公开课 - 博弈论课程节选

So if Player I chooses 4, Player II should choose, I'm sorry, Player II chooses 4, player I should choose 2, and this is a straight line in between.

如果参与人I选4,参与人II要,说错了,是参与人II选4而I选2,这两点之间是一条直线

耶鲁公开课 - 博弈论课程节选

The way we read this graph, is you give me an S2, I read across to the pink line and drop down, and that tells me the best response for Player I.

这个图的作用是,给定一个S2,找到粉线对应的坐标,然后就能找出参与人I的最佳对策

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

Now we can do the same for Player II, we can draw Player II's best response as it depends on the choices of Player I, but rather than go through any math, I already know what that line's going to look like.

同理也可以画出参与人II的图像,参与人II的最佳对策,取决于参与人I的策略,不用任何数学的方法,我就知道图像是什么样的了

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