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The first one is Dr. Marvin Chun who teaches the Introduction to Psychology course in the fall and is my competition.
第一名是马文·春博士,他会在秋季教授心理学导论课程,也是我的竞争对手
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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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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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I get all the voters right on top of me at position 1 and she gets everyone else, is that right?
我得到选择立场1的10%选票,对手得到剩余90%的选票,对吗
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The payoff of 2 against 3 is all the people at 1, all the people at 2, so it's 20%.
如果对手选3而我选2我会得到,立场1和2的全部选票,一共20%
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So by thinking about my opponent, by putting myself in my opponent's shoes, I realize that she has a dominant strategy, Alpha.
所以考虑到我的对手,站在她的立场上看,我发现她有一个优势策略α
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Then we're going to compare my payoff from choosing 1 against the other candidate's payoff from choosing 1.
我们来计算当对手选立场1时,我也选立场1获得的收益
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And we've already agreed that if I think it's equally likely they're going to choose right and left, that there's a probability ?
而且我们已经计算过了,如果我觉得对手,选左选右的概率相同,即他们选右的概率为1/2时
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Against 3: so now we're comparing my choosing 1 versus 3 and my choosing 2 versus 3.
对手选立场3,现在来计算我选立场1对手选立场3,或者我选立场2对手选立场3的情况
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Conversely, if there was probability 1 that the other guy is going to choose Right, and I choose Up, then I get 0.
相反,如果对手,选择右的概率为1,并且我选的是上,那我的收益为零
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Once again the row player is the first payoff and the column player is the other payoff.
这次还是第一个收益是我的,另一个收益是我对手的
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We're going to compare this with my payoff from choosing 2 against the other candidate choosing 1.
我们再计算当对手选择立场1时,我选择立场2获得的收益
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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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I might not be sure whether the opponent, whether my opponent, is choosing Left or Right.
我可能不太确定,我的对手会选择左还是右
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So this point here corresponds to my payoff if I choose Up and they choose Right.
也就是说这个点表示,我选上对手选右时我的收益
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So what's my expected payoff from choosing Up where I believe the other person's going to choose Left and Right, equally likely? It's what?
那么在我对手选择左或右,可能性相同的情况下,我的预期收益会是什么样的呢
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While we're here, let's just mention that things will get more complicated in a world where I don't actually know the payoffs of my opponent.
现实中我并不知道,我对手的收益到底是什么样的,这会使事情变得更加复杂
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So this is my grades on the left hand table, but now let's look at what my pair will do, what my pair will get.
我的成绩写在左边的表格里,我们再看看我对手,她会得到什么成绩
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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 believe the other guy is going to choose Left, I can rationalize choosing Up.
我认为对手应该会选左,这样我认为选上是合理的
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Let's look at my payoffs from choosing these three options Up, Middle, and Down, if I think it's equally likely that my opponent will choose Left and Right.
我们来看一下我从上中下这三个策略中,分别能获得什么样的收益,如果我认为我对手,选择左或右的可能性相同
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We had acknowledged that Alpha is a dominant strategy for my opponent so we must choose based upon, or knowing that my partner is going to choose Alpha.
我们发现了α是我们对手的优势策略,所以我们必须要根据,我对手会选α来做出选择
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My opponent or my partner's payoffs come from the indignant angel matrix.
我的对手或者收益是愤怒天使的收益
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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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The first grade corresponds to the row player, me in this case, and the second grade in each box corresponds to the column player, my pair in this case.
单元格内第一个成绩是我的成绩,每个单元格第二个成绩是,我对手的成绩
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And my opponent's payoffs are what would have been my payoffs before.
我对手的收益是,我上个博弈的收益
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But look at my opponent. My opponent's Alpha dominates her Beta.
但是对我的对手来说,选α优于β
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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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Well now I need to be rational, I need to know that other people are rational, and I need to know that other people know that other people are rational.
我自己已经是理性的了,我也知道对手也是理性的,我还需要知道对手们明白,他们的对手也是理性的
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What about my expected payoff from choosing Middle against , so in this case where I think it's equally likely that my opponents going to choose Left or Right?
那我在情况下,选中的预期收益是什么呢,在此情况下我依然认为,对手选左选右的可能性相同
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