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So Alpha in this case is better against Alpha, and Beta is better against Beta, but neither dominates each other.
所以对方选α时我应该也选α,她选β我也应该选β,这里没有优势策略
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She said, no matter what the other person does, she reckons she'd get a better grade if she chose Alpha.
她说无论别人怎么选,她觉得选α会使自己得到最优的结果
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I choose; c'est entendu?" she said, wobbling a little beside me.
我来选地方，说定了？“她问，在我身边轻微的颤抖着。
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And here if I choose 2 against 4, I get all the people at 1, all the people at 2, and what?
如果我选2她选4呢,我会得到立场1和2的选票
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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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If the pair chooses Beta, then if she chooses Alpha she gets 3, Beta she gets 1, and 3 is bigger than 1.
如果她对手选β,她选α得到3,她选β得到1,3也比1大
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So in both cases, no matter what the other person does, she receives a higher payoff from choosing Alpha, so she should choose Alpha.
这两种情况下,无论别人怎么选,她选α总能得到更好的成绩,所以她应该选α
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She's going to choose Alpha and my best response against Alpha is to choose Alpha myself.
她会选α,介于此情况,我最好也选α
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So I could communicate with Alice on agreements, but back home I'm going to go ahead and choose Alpha anyway; all the better if she's choosing Beta.
所以我可以和爱丽丝说好了,但回家之后我还是可以选α的,要是她还选β那就更好了
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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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If the pair chooses Alpha and she chooses Alpha, then she gets 0.
如果对手选α她也选α,她得到0
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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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Beta is better against Beta. There's no dominance going on here.
她选β我也应该选β,这次没有优势策略
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As we saw before, Alpha is better against Alpha.
就像我们看到的,她选α我最好选α
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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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Good; so what Clara Elise is saying--it's an important idea-- is this and tell me if I'm paraphrasing you incorrectly is no matter what the other person does, no matter what the pair does, she obtains a higher payoff by choosing Alpha.
克莱拉?埃莉斯得意思是,要是我转达的不对请提示我,不管别人怎么选,不管她对手选了什么,她选α总会得到最优的成绩
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So the woman, I have immediately forgotten the name of, in the red shirt, whose name was Courtney, so Courtney also gave a reason for choosing Alpha, and it was a perfectly good reason for choosing Alpha, nothing wrong with it, but notice that this reason's a stronger reason.
我忘记刚才那位女士的名字了,穿红色衬衫的那位,她叫考特尼,对,考特尼也说了她为什么选α,她也有不错的理由来选α,这本身没错,但是呢,这个理由显得更充分
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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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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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If I put Alpha and my pair puts Beta, then she gets a C.
如果我选α我对手选β,那么她得C
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And if I put Beta and she puts Alpha, then she gets an A.
如果我选β她选α 那么她得A
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If I put Alpha and she put a Beta, I got an A, and if I put Beta and she put an Alpha, I got a C.
如果我选α她选β 我得A,如果我选β她选α 那么我得C
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So Player I's payoff, if she chooses top and Player II chooses center, we read by looking at the top row and the center column, and Player I's payoff is the first of these payoffs, so it's 11.
参与人I的收益,如果她选上,参与人II选中,我们来看一下上行和中列,参与人I对应第一个收益即11
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I'll say it again, Player i's strategy "s'i" is weakly dominated by her strategy "si" if she always does at least as well by choosing "si" than choosing "s'i" regardless of what everyone else does, and sometimes she does strictly better.
重申一下,参与者i的策略s'i,弱劣于策略si,当且仅当无论对手怎么做,她选择si的收益至少与选s'i的相等,有些情况下甚至是严格占优的
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Conversely, if I chose a Beta and my pair chooses an Alpha, so I end up with a C and she ends up with an A, then you know I have a bad time explaining to my parents why I got a C in this class, and I have to say about how I'm going to be president anyway.
相反如果我选β我对手选α,我得到C她得到了A,我回家后很难跟父母,解释为什么我只得到了C,然后我还得表示下雄心壮志
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