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If my opponent chooses Beta and I choose Alpha, I get 3; Beta, I get 1. Once again Alpha is better.
如果我对手选β,我选α我得3,选β我得1,也是选α好
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Let's just check. If my pair chooses Alpha, then my choosing Alpha yields 0, Beta -3: so Alpha would be better.
我们来验证下,如果我对手选α,我选α得0,选β得-3,所以选α更好
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On the other hand, when it came to penetrating solids, penetrating solids, the alpha radiation was poor at penetrating solids, whereas the beta radiation was very good at penetrating solids.
另一方面，当研究穿过固体的时候，嗯，穿过固体，会发现阿尔法射线很难穿过固体，然而贝塔射线,很容易穿过固体。
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So Alpha does better. But if my pair chooses Beta, then Alpha gets me -1; Beta gets me 1.
此时选α较好,但是如果我对手选β,我选α得-1,选β得1
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But if my pair chooses Beta then Alpha yields -1, Beta yields 1: in this case Beta would be better.
但是要是我对手选β我选α得-1,选β得1,此时选β更好
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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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The reason I chose Alpha, regardless of what my partner chose, I think there would be better outcomes than choosing Beta.
我选α是因为不管我对手选什么,我选α得到的成绩总会比选β的要好
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If I choose Alpha and she chooses Alpha to get 0; Beta she gets -1. Alpha is better.
如果我选α,她选α她得0,选β她得-1,选α更好
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It's still I'm choosing Alpha and Beta, my pair is choosing Alpha and Beta, and the grades are the same as they were before.
还是我选α和β,我对手选α和β,成绩的评判和之前是一模一样的
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If I choose Beta, if she chooses Alpha she gets 3; Beta 1.
如果我选β,她选α得3,选β得1
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We say that my strategy Alpha strictly dominates my strategy Beta, if my payoff from Alpha is strictly greater than that from beta, regardless of what others do."
无论别人怎么选,如果选α得到的结果严格优于β,那么α相对于β是个严格优势策略"
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If my pair chooses Alpha then Alpha gets me 0; Beta -3.
如果我对手选α那么我选α得0选β的-3
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All right, so here once again is our same matrix with me and my pair, choosing actions Alpha and Beta, but this time I'm going to put numbers in here.
我们首先讨论我和我对手,选择α或β的矩阵,不过这次我们用数字来表述
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We pointed out, that in this game, Alpha strictly dominates Beta.
我们指出,此博弈中α严格优于β
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If the pair chooses Alpha and she chose Beta, she gets -1.
对手选α她选β,她得到-1
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Again Alpha is better. For my opponent, alpha dominates Beta.
选α还是比β好,对我对手来说,α优于β
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Regardless of what the other person does. Alpha dominates Beta.
不管别人怎么选,α优于β
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No, in fact, alpha doesn't dominate Beta for me.
没有,对我来说选α并不优于β
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Let's try here: Alpha, Beta, alpha, Beta, pair, me.
先写上 α β 对手,我
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And once I know that she's going to choose Alpha, it's clear that I should choose Alpha and get 0 rather than Beta and get -3. So I should choose Alpha also.
一旦我意识到她会选α的时候,很显然我应该也选α来得到0单位效用,而不是选β只得到-3,所以我也选α
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My Alpha doesn't dominate my Beta.
我选α并不优于选β
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So Alpha dominates Beta here.
这里α还是优于β的
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Does my Alpha dominate my Beta?
我选α优于选β吗
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What I'm gonna do is draw a larger table, the same basic structure: I'm choosing Alpha and Beta on the rows, my pair is choosing Alpha and Beta on the columns, but now I'm going to put both grades in.
我要画个结构相同的大表格,用列来表示我选α还是β,用行来表示我对手选α还是β,但我要把两人成绩写在一个单元格里
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So what I'm going to do is I'm going to put me here, and my pair, the person I'm randomly paired with here, and Alpha and Beta, which are the choices I'm going to make here and on the columns Alpha and Beta, the choices my pair is making.
那么我把我写在这里,我对手,就是被随机分到的人写在这,还有是α和β,就是我要做的选择,还有我对手要做的选择
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I mean if you chose Alpha, you're swinging from A to B-; and from Beta, swinging from B+ to C.
要是你选α,你的分数会在A到B-,选β,分数范围会在B+到C
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But if I choose Alpha and my pair chooses Beta, I get an A and she gets a C.
要是我选α我对手选β,我得A 她得C
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If you put Beta and you're paired with Alpha, you'll get a C and your pair an A.
如果你选β你对手选α,你得C你对手得A
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And if I choose Beta and she chooses Alpha, then it's me who gets the C and it's her who gets the A.
如果我选β她选α,我得C而她得A
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So my grade if we both put Alpha is B-, if we both put Beta, was B+.
如果我们都选α我得B-,都选β我得B+
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