We said players should never play a strategy that's never a best response to anything, so we threw those away.

我们学到了参与人不应该选择,非最佳对策的策略,应该剔除它们

耶鲁公开课 - 博弈论课程节选

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

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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

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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

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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

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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

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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

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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

The players are playing a best response to each other.

参与人们都采用了自己的最佳对策

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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

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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

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We learned that in this game deleting strategies that are never best response, and then deleting strategies that are never best response to anything that is a best response and so on and so forth, yielded a single strategy for each player.

我们学到了在剔除,非最佳对策的策略后,要再剔除那些在对手最佳对策下,不是最佳对策的策略,以此类推,最后每个参与人都只有一个策略了

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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

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I'm going to put down two different definitions of best response, one of which corresponds to best response to somebody else playing a particular strategy like left and right, and the other is just going to correspond to the more general idea of a best response to a belief.

我写出最佳对策的两种不同形式定义,一个是参与人针对对手策略的定义,比如这里的左路右路,另一个强调的是,最佳对策的广义上的定义

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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

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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

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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

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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

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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

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So if Player I chooses S1*, Player II will want to choose S2* since that's her best response.

所以当参与人I选择S1*时,参与人II就会选择最佳对策S2

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If Player II is playing S2*, Player I will want to play S1* since that's his best response.

如果参与人II选择S2,参与人I就会选最佳对策S1

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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

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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

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, 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

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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

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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

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How are we going to figure out what Player i's best response is? Shout loudly.

请大声说如何找出参与人I的最佳对策

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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

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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

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Put another way, what strategies of Player I's are ever a best response?

换句话说,参与人I的哪些策略,永远不会成为最佳对策

耶鲁公开课 - 博弈论课程节选