We said players should never play a strategy that's never a best response to anything, so we threw those away.

我们学到了参与人不应该选择,非最佳对策的策略,应该剔除它们

耶鲁公开课 - 博弈论课程节选

Player II has three choices, this game is not symmetric, so they have different number of choices, that's fine.

参与人II有三种选择,这个博弈不是对称的,所以他们可选策略数量不同,这无所谓

耶鲁公开课 - 博弈论课程节选

And if Player I chooses bottom, then center yields 2, right yields 0: 2 is bigger than 0 again.

如果参与者I选择下,选中的收益是2,选右的收益是0,2大于0

耶鲁公开课 - 博弈论课程节选

Player II has three choices left, center, and right, represented by the left, center, and right column in the matrix.

参与人II有三种选择,左中右,用矩阵的左中右三列来表示

耶鲁公开课 - 博弈论课程节选

So if Player I chooses S1*, Player II will want to choose S2* since that's her best response.

所以当参与人I选择S1*时,参与人II就会选择最佳对策S2

耶鲁公开课 - 博弈论课程节选

If Player II is playing S2*, Player I will want to play S1* since that's his best response.

如果参与人II选择S2,参与人I就会选最佳对策S1

耶鲁公开课 - 博弈论课程节选

If Player I chose top, center yields 3, right yields 0: 3 is bigger than 0.

如果参与者I选择上,选中的收益是3,选右的收益为0,3大于0

耶鲁公开课 - 博弈论课程节选

For instance, if Player II picks left then Player I wants to pick bottom, but if Player II picks center, Player I wants to pick center.

例如,参与者II选择左,参与者I会选择下,但是若参与者II选择中,参与者I会选择中

耶鲁公开课 - 博弈论课程节选

So here Player I's strategy set, she has two choices top or bottom, represented by the rows, which are hopefully the top row and the bottom row.

这是参与人I的策略集合,她有上下两种选择,用横排来表示,即上下两排

耶鲁公开课 - 博弈论课程节选

Imagine you're Player I in this game, what do you think you'd do?

现在假设你就是参与人I,你认为你应该怎么选择呢

耶鲁公开课 - 博弈论课程节选

This is the payoff to Player I of choosing Middle against Left.

这条线表示参与人I在对手选右时,选择左而获得的收益

耶鲁公开课 - 博弈论课程节选

It involves two players and we'll call the Players I and II and Player I has two choices, top and bottom, and Player II has three choices left, center, and right.

此博弈有两个参与人,分别为I和II,参与人I有两个选择,上和下,参与人II有三个选择,左中右

耶鲁公开课 - 博弈论课程节选

The highest Player II ever chooses is 2, and the highest response that Player I ever makes to any strategy 2 or less is 6/4, so all these things bigger than 6/4 can go.

参与人II最大只会选策略2,参与人I针对这种情况下,最大只会选择6/4,即大于6/4的策略也会被剔除

耶鲁公开课 - 博弈论课程节选

So here's the straight line, and this line is the expected payoff to Player I from choosing Down as it depends on the probability that the other person chooses Right, and then once again, we can write down the equation.

这就是第三条直线了,它表示参与人I选择下获得的收益,是另一个参与人,选右概率的一个函数,对于这一条直线,我们依然能够给出方程式

耶鲁公开课 - 博弈论课程节选

So to say it in words, Player i's strategy "s'i" is strictly dominated by her strategy "si," if "si" always does strictly better -- always yields a higher payoff for Player i -- no matter what the other people do.

用文字来描述就是,参与人i的策略s'i严格劣于si,如果si总是更好的选择,即总能给参与人i带来更高的收益,而无论其他参与人怎么选

耶鲁公开课 - 博弈论课程节选