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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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it's going to be: 1 minus the probability they'll choose Right times 1, plus the probability that they choose Right times 4.
方程是,1减对手选右的概率再乘以1,加上对手选右的概率乘以4
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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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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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And we know that Down does best if I think it was equally likely that the person was going to choose Left and Right.
我们还知道如果我们认为对手,选左或者是右的可能性相同的情况下,下是此情况下最好的策略
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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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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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It's my belief that the other guy's going to choose Right.
也就是我关于对手选右概率的信念
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So if the other person's choosing Right with probability 0, that's the same as saying they're going to choose Left, and if I chose Middle against Left, I get what?
如果对手选右的概率是0,也就是说对手选左,此时我选中的收益是什么
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It's the safer answer if you can't decide whether or not your opponent's going to choose Left or Right, so you don't have to worry about having a payoff of 0.
当你无法判断你的对手会选左还是右时,选下是较安全的答案,因此你不必担心收益变成0
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So this isn't so hard, we know that if I choose Up and there's probability 0 that the other guy is going to choose Right, that's the same as saying I choose Up and the other guy chooses, let's try it again.
这不是很难得,我们知道如果我选上的话,我对手选右的概率就是0,也就是说我选上,我对手会选择,我说错了,重新来
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Or on the other side, there's a debate about whether Mitt Romney can choose to be, I guess he's trying to choose himself to be on the right hand wing of the republic party, given he has a record of governance, as being governor of Massachusetts when he provided state healthcare for example.
或者在另一派,争论米特·罗姆尼是否会选择,我猜他试图选择作为,右派共和党,考虑到他的政绩,在他作为马萨诸塞州州长期间,他提供了的州卫生保健
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So this is a subtle thing because you think about the current election, there's a debate about whether Hilary Clinton, for example, can choose right now to be at the center of the democratic party given her past history of votes, for example, on the Iraq War.
这是个微妙的事情,因为你联想到现在的选举,举个例子,关于希拉里·克林顿能否选择,作为民主党竞选中间派参选就颇有争议,考虑到她的参选记录,例如在伊拉克战争中
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If I think the probability that they're going to choose Right is less than X, then my best response is to choose Up.
也就是说如果我觉得,对手选右的概率小于X,那我的最佳对策是选上
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It's more likely than Y the probability that they're going to choose right is more than Y, then the highest line of these three is this one, which corresponds to my choosing Middle.
即比Y大,也就说对手选右的概率大于Y,那么这三条线中最高的是这条线,这条线表示我选中的收益
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This is the payoff to Player I of choosing Middle against Right, and the line in between, this line here, is the expected payoff to Player I of choosing Middle as a function of the probability that other people choose Right.
这条表示对手选右时参与人选中的收益,两个端点中间的线段部分,表示参与人I选右的预期收益,它是对手选右概率的一个方程
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