So what is this? This is Player 2's best response, so Player 1's best response to Player 2 producing half monopoly output.

这是什么,这是参与人2的最佳对策,即参与人1对于2半垄断产量的最佳对策

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

So, in particular, what would be Player 1's best response if Player 2 didn't produce at all?

比如说,参与人2产量为0时1的最佳对策是什么

耶鲁公开课 - 博弈论课程节选

This was the best response of player 1 and this was the best response of Player 2.

这是参与人1的最佳对策,而这是参与人2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

The more Player 1 produces, the less player 2 wants to produce and the more Player 2 produces, the less Player 1 wants to produce.

参与人1的产量越多,参与人2就会减产,如果参与人2增产,那么参与人1就要减少产量

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

If Player 2 is producing nothing, then what is Player 1 effectively?

参与人2产量为0,参与人1会怎样呢

耶鲁公开课 - 博弈论课程节选

What is Player 1's best response? Someone read it off for me.

谁来说一下,参与人1最佳对策是什么

耶鲁公开课 - 博弈论课程节选

In that game, if you remember what the best responses looked like, they looked like this where this was the effort of Player 1; this was the effort of Player 2.

不知道你们还记不记得最佳对策是什么了,这条线代表参与人1的付出,这条代表参与人2的付出

耶鲁公开课 - 博弈论课程节选

So Nina's preferences are Player 1's preferences here.

妮娜的偏好就是参与人1的偏好

耶鲁公开课 - 博弈论课程节选

This is the best response of Player 1 to the best response of Player 2, to the best response of Player 1 to Player 2 producing half monopoly output and there are lots of brackets here.

它表示参与人1对于参与人2的最佳对策,是参与人2生产垄断产量一半的情况下的,这里有一大堆的括号

耶鲁公开课 - 博弈论课程节选

So this is going to be the choice of Player 1, and this is going to be the choice of Player 2, and what I want to do is I want to figure out what this looks like.

这个表示参与人1的策略,这个表示参与人2的策略,接下来我想要知道,这个函数究竟是什么样子的

耶鲁公开课 - 博弈论课程节选

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

Both people would rather be at an equilibrium than to be mal-coordinated or uncoordinated, but Player 1 wants to go to Bourne ultimatum and Player 2 wants to go to Good Shepherd, and actually I thought Nina's strategy there was pretty good.

每个参与人都觉得达成均衡,总比协调失败要好得多,但是参与人1想看《谍影重重》,而参与人2想看《特工风云》,我觉得妮娜的策略很好

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

What's that telling me is that if Player 2 chooses not to produce then Player 1's best response is a - c over 2b.

参与人2产量为0而参与人1最佳对策是,/2b,这能说明什么

耶鲁公开课 - 博弈论课程节选

For each q2 that you give me or that Player 2 chooses, I want to find out and draw what is Player 1's best response.

对与参与人2的每个策略q2,我想知道参与人1的最佳对策是什么

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

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

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 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

If Player II chooses 0 then Player I's best response is 1, and that's as low as he ever goes.

参与人II选0时参与人I最佳对策是1,这是最小值了

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

If I'm careful I should get this right 1, 2, 3, and 4 are the possible choices for Player I.

我好好画一下,这样会准确点,参与人I的可选策略从1一直到4

耶鲁公开课 - 博弈论课程节选

, okay. So 1 plus 1/4 of 0 is 1, so if Player II chooses 0, player I's best response is to choose 1.

是1,因为1+0/4=1,参与人II选0时I的最佳对策是1

耶鲁公开课 - 博弈论课程节选

So these strategies down here less than 1 are never a best response for Player I.

参与人I的小于1的策略,永远都不会成为最佳对策的

耶鲁公开课 - 博弈论课程节选

So the strategies below 1 and above 2 are never a best response for Player I.

也就是说小于1及大于2的策略,都不是参与人I的最佳对策

耶鲁公开课 - 博弈论课程节选

So it'll be 1 plus 1/4 times 4, 1/4 times 4 is 1, so 1 plus 1 is 2, so Player II's best response in that case will be 2.

这回就是1+4/4,即1+1=2,所以此时参与人II的最佳对策是2

耶鲁公开课 - 博弈论课程节选

So we're throwing away all of the strategies less than 5/4 for Player I and bigger than 6/4 for Player I, which is 1? for Player I and similarly for Player II.

这样我们又剔除了,参与人小于5/4大于6/4的策略,参与人I只有1?的区间,同理可证参与人II

耶鲁公开课 - 博弈论课程节选