What I did was I took the ten best-performing Internet funds and looked at the returns from 1997 to 2002.

我选了十个表现最好的投资网络的基金,分析它们1997至2002年的收益情况

耶鲁公开课 - 金融市场课程节选

So in this case, my expected payoff is a ? of 1 plus a ? of 4, for a total of again 2.5.

在这种情况下,我预期收益是?乘1加?乘4,总和还是2.5

耶鲁公开课 - 博弈论课程节选

You want to, for any given expected return, you want to minimize the standard deviation, so it's the left-most line and that means that everyone will be holding the same portfolio.

你希望，在期望收益固定的情况下，你肯定希望将标准差最小化，而这条线是最左边的线,这就意味着所有人,都愿意持有这样的投资组合。

耶鲁公开课 - 金融市场课程节选

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

耶鲁公开课 - 博弈论课程节选

So I promised a while ago now, that we were going to come back and look at this game under some other possible payoffs.

我保证,我们以后还会讨论这些在,其它博弈下的收益情况

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

Now, we're going to go back to Roger Ibbotson at the School of Management. He did some path breaking work in terms of describing capital markets returns over reasonably long periods of time.

先讲回到管理学院的罗格·伊博森,所进行的开创性研究,描述了在相当长的时期内,资本市场的收益情况

耶鲁公开课 - 金融市场课程节选

How about my expected payoff from choosing Down versus ?

那在情况下我选下的预期收益呢

耶鲁公开课 - 博弈论课程节选

Probability is 0 of their choosing Right is the same as saying they choose Left, so that my payoff from Up against that is given by the top box up there, I get 5.

如果对手选右的概率是0,其实就是说他们会选左,因此此情况下我选上的收益,从上面的矩阵看,我的收益是5

耶鲁公开课 - 博弈论课程节选

The equally-weighted case that I gave a minute ago was one where the two assets had--were at the same-- had the same expected return and the same variance; but this is quite a bit more general.

我刚刚举的相同权重的例子,表示两种资产-,有相同的预期收益和相同的方差;,但这种情况更加普遍一些。

耶鲁公开课 - 金融市场课程节选

And we already know if I look at the probability of a ?, which is here, that the payoff I get from choosing, the expected payoff I get from choosing up against a is 2.5.

我们已经计算过了概率是?的情况,即在对手概率是的情况下,我选择上我从中获得的,预期收益是2.5

耶鲁公开课 - 博弈论课程节选

So, for example, at an annual expected return of 12% if I have a portfolio of stocks, bonds, and oil I can get a standard deviation of something like 8% on my portfolio.

例如，在年预期收益12%的情况下%,我有股票，债券和石油的投资组合,在这个组合里,我的投资组合可以取到8%的标准差。

耶鲁公开课 - 金融市场课程节选

Player II's payoff, from the same choices, top for Player I, center for Player II, again we go along the top row and the center column, but this time we choose Player II's payoff, which is the second payoff, so it's 3.

在这种情况下参与人II的收益,即参与人I 选上参与人II选中时,注意下是上行和中列,但是现在我们要找参与人II的收益,也就是第二个收益,即3

耶鲁公开课 - 博弈论课程节选

So strategy ?i is a best response to the strategy S-i of the other players if my payoff from choosing ?i against S-i, is weakly bigger than that from choosing Si' against S- i, and this better hold for all possible other strategies I could choose.

策略?i是其他参与人策略S-i的,最佳对策,如果此时我选?i的收益,弱优于此情况下选Si'的收益,这对于所有我可以选择的策略都成立

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选