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For example, I could believe that it's twice as likely that the person's going to choose Left as Right.
比方说,我可能认为对手选左的可能性,是选右的可能性的2倍
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Who would choose Beta? Very few Beta's, but mostly Alpha's. Alpha, I think, is the right answer here but why?
好,谁会选β,很少有选β的,基本都选的是α,α应该是正确答案
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If the program works right here's what people said, 81% said pneumonia, 15% malaria, 2% cancer, and 2% heart disease.
如果程序没出错,你们的选择是这样的,81%选了肺炎,15%疟疾,2%癌症和2%心脏病
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One is the first volume of The Norton Anthology of Modern and Contemporary Poetry, Third Edition.
其中有一本,是第三版的《诺顿现代诗歌选》
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You can't do it because, I don't do mornings or because my girlfriend is in this other section.
你不能只是因为，我不想上早上的课因为我女朋友,选的是另一个时间的课。
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But it turns out actually over a third of people who took this class last year took the class because they felt depressed.
但是结果是去年有超过三分之一的人,选这门课是因为他们感觉抑郁。
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p2 It would stop there because we've chosen p2.
因为我们选的压强是。
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That means that you want to pick, ultimately, a point on this-- this line is tangent to the efficient portfolio frontier with all the other assets in it.
那意味着你会最终会在这上面选一个点-,这条直线是与有效边界相切的,后者包含了所有的资产组合。
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Because we've just sat in lecture and you've told us we're not being rational if we pick a high number.
因为我们刚刚上过课,你告诉我们选大数的人是不理性的
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I guarantee, more than that In fact, the people who chose where we started off 33 chose in that range.
我保证,多很多的,实际上选33的人是在这个范围内选择的
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So the probability is 0 of the other guy choosing Left is, the same as, let's try it again.
同样的如果对手选左的概率是0,那也就是说,重新来
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Two-thirds of the average was 9 and some of you chose 9, so if you are here, stand up.
平均值的2/3是9,有人选了9,所以如果你选了9请起立
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Because I thought the payoffs - the two different payoffs that I could have gotten-- were highest if I chose Alpha.
因为我发现,如果我选α的话,我得到的两种结果是最优的
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All of you chose Down, but Up does best against Left and Middle does best against Right.
你们都选择下,可是选上是左的最佳对策,而选中是右的最佳对策
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If this probability is 0 that the other guy chooses Right, that's the same as saying that the other guy is going to choose Left.
如果对手选右的概率是0,也就是说我认为对手绝对会选左
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I want to inspire you to take some more advanced courses albeit in another department.
我想鼓励你们选一些更深入的课程,尽管那是别的学院开的课
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Nevertheless, at least 90% of you chose Alpha here, and that's the right answer.
然而90%以上的人都选了α,选α是正确的答案
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The reason I don't want to play a strictly dominated strategy is, if instead, I play the strategy that dominates it, I do better in every case.
我不选择严格劣势策略的原因是,要我选了优势策略,我在每次博弈都得到更好的收益
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so in some sense it's safer, it avoids the 0, although I mean it's true it avoids the 0 but it also doesn't get the 5 and the 4.
某些情况下选下是比较安全的,因为他避免了0收益,我的意思是它的确避免了0收益,但选它也得不到5和4这连个最大收益
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It could be, they're twice as likely to choose Left as Right.
这也可能啊,选左可能性是右的2倍
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okay I chose Middle because I believed that the other guy was going to choose Right and Middle was the best thing for me to do against Right."
我选中是因为,我认为另一个人会选右,并且选中是右的最佳策略
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We've argued that 1 and 10 shouldn't be chosen because they're dominated.
我们已经知道无人会选立场1和10,因为它们是劣势策略
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Against 4, the payoff from choosing 2 against 4 is what?
对手选4而我选2的收益是什么呢
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So this is my payoff from choosing Up against Left.
这是我选上对手选左时我的收益
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If I thought there was 2/3 probability they'd choose Left and 1/3 probability they'd choose Right, then I think it's twice as likely they're going to choose Left, and I could redo this calculation.
如果你觉得对手选左的可能性是2/3,而选右的可能性是1/3,即对手选左的可能性是右的2倍时,我们再重新计算一下
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the winner is the person whose number is closest to 2/3 times the average The winner will win $5 minus the difference in pennies between her choice and that two-thirds of the average."
所选数字最接近2/3倍平均数人是赢家,赢家的奖金是5美元减去,所选数和平均数三分之二之差的百分数
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Everyone agree because 5 is bigger than 1, and 5 is bigger than 4, so Up is and to use a technical term we'll define formally next time Up is the best response to Left.
大家都知道5大于1,5也大于4,所以选上是,以后我们就要用术语来说了,选上是左的最佳对策
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By the way, when we turn in concept sheets each week you'll have the option of turning them in either on Monday or on the Wednesday of that week, whenever you choose to do it is fine.
顺便说下,当我们每周收观点报告时,你们可以在当周周一,或者那周三上交,无论你选哪一天都是可以的
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