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Even though the best response is pretty complicated-- and by the way, obviously the things are symmetric for Payer II.
虽然最佳对策是很复杂的,顺便说一下 选手2的情况也明显是这样
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Even though these best responses are pretty complicated it turns out that there's only one Nash Equilibrium in this game.
虽然最佳对策是很复杂的,在这个博弈中却只有一个纳什均衡
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That is one of the major points as to why deafness has not gotten a cure yet.
这就是到目前为止,还没有对策的一个主要原因。
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Zero profits, I'll make zero profits, so that certainly is a best response, pricing at marginal cost as well.
零利润,我将没有利润,所以这确实是一个最佳对策,也定价在边际成本
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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
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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
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Again, how much quantity would Firm 2 have to produce in order to induce Firm 1's best response to be 0?
重复一遍,公司2的产量是多少时,公司1的最佳对策是产量为0呢
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I threw away all strategies that were never a best response, then I looked at the strategies that were left.
我剔除了非最佳对策的策略,然后我看看还剩下哪些策略
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Each of them is trying to play a best response for what they anticipate the other person's going to do.
每家公司都想采取预料的对方策略的,最佳对策来制定产量
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Now we're going to analyze this, no secret here, we're going to analyze this using the idea of best response.
毫无疑问,接下来,我们要用最佳对策的思想来分析了
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I go up to the green line and go across and this tells me the best response for Firm 2.
根据这条绿线的对应法则,就可以对应出公司2的最佳对策
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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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So I want to figure out the best response of Firm 1 as a function of the price chosen by Firm 2.
我想找出公司1的最佳对策,并用公司2价格的函数表示
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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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Say it again: if everyone chose 1, then everyone's best response would be to choose 1, so that would be a Nash Equilibrium.
重复一下,如果每个人都选了1,那么每个人的最佳对策也就是1,这就会成为纳什均衡
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So what we're going to do together is to figure out what these best responses look like and let's try and do that.
所以我们将一起找出,最佳对策是什么,我们一起试着找找
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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 last time we introduced a new idea and the new idea was that of best response.
上一讲我们引入了一个新概念,这个新概念就是最佳对策
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The strategies I'm about to throw away now, they're not--it isn't that they're not best responses, they are best responses to something.
我要剔除的策略,并非都不是最佳对策,它们可能是某种情况下的最佳对策
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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 I should cheat and pick the quantity on my best response line that's much farther out so I'll produce more than my quantity.
我会违约选择我最佳对策的产量,我会生产出远远多于协约量的产品来
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So here is the best response of Firm 1 to each possible choice of Firm 2.
这是公司2每种策略下公司1的最佳对策
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But the things they were best responses to, we know are not going to be played, because they themselves were not best responses to anything.
我们都知道使他们成为最佳对策的策略,是不会有人采用的,因为这些策略本身又不是最佳对策
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So if Firm 2 produces this amount then Firm 1's best response is this amount.
如果公司2的产量是这么多,那么公司1的最佳对策就是这个产量
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Let's think about Firm 2, is Firm 2 playing a best response to Firm 1?
我们从公司2的角度想一下,公司2针对公司1给出了最佳对策吗
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If you took a best response to some believe, you can say I took this action because I believed other people are going to do this.
如果你针对自己的信念做出了最佳对策,你就可以说,我是所以这么做,是因为我认为其他人会那么做
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If Firm 2 produces this amount then Firm 1's best response is this amount.
如果公司2的产量是这么多,那么公司1的最佳对策就是这个产量
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So to find the Nash Equilibrium we're going to have to find best responses.
为了找到纳什均衡,我们必须找到最佳对策
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And in particular, I want to be formal about the definition of best response.
尤其是,我想给出最佳对策的正式定义
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