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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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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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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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

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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

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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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So suppose Player 2 doesn't produce at all.

假如参与人2产量为0

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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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So her best thing now is to successfully meet David at The Bourne Ultimatum and David's preferences are Player 2's preferences, so his favorite thing is to successfully meet at The Good Shepherd.

她最希望和大卫一起看《谍影重重》,大卫扮演参与人2,他最想和妮娜一起看《特工风云》

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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

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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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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

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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

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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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I'll just remind us of what these functions are; it's a - c over 2b - q2 over 2 and accordingly for Player 2.

再说一遍,参与人2的方程是,/2b - q2/2

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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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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

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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

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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

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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

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And if Player I chooses bottom, then center yields 2, right yields 0: 2 is bigger than 0 again.

如果参与者I选择下,选中的收益是2,选右的收益是0,2大于0

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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

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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

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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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And the strategies above 2 were never a best response for Player II.

大于2的也不是参与人II的最佳对策

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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

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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

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The highest Player II ever chooses is 2, and the highest response that Player I ever makes to any strategy 2 or less is 6/4, so all these things bigger than 6/4 can go.

参与人II最大只会选策略2,参与人I针对这种情况下,最大只会选择6/4,即大于6/4的策略也会被剔除

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