We're going to converge in, in this game, to just one strategy for each player, which is where they intersect.

这个博弈最后会归为一点,每个人只有一个策略,就是交点处

耶鲁公开课 - 博弈论课程节选

Identify the best responses of each player as a function of the others and find out where they intersect.

把每个人的最佳对策看成别人策略的函数,然后找出函数的交点

耶鲁公开课 - 博弈论课程节选

Just one strategy for each player and that strategy was given by this equation.

每个参与人只有一个策略,而那个策略是这个方程的解

耶鲁公开课 - 博弈论课程节选

What it's saying is one strategy for each player in the game.

他表示每个参与人都有一个对应的策略

耶鲁公开课 - 博弈论课程节选

Each player prefers a different Nash Equilibrium.

每个参与人偏爱不同的纳什均衡

耶鲁公开课 - 博弈论课程节选

We learned that in this game deleting strategies that are never best response, and then deleting strategies that are never best response to anything that is a best response and so on and so forth, yielded a single strategy for each player.

我们学到了在剔除,非最佳对策的策略后,要再剔除那些在对手最佳对策下,不是最佳对策的策略,以此类推,最后每个参与人都只有一个策略了

耶鲁公开课 - 博弈论课程节选

Good, so what I have here is an equation that tells me Player 1's best response for each possible choice of Player 2.

这个方程表示,参与人2不同策略下参与人1的最佳对策

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

So what we're going to do is we're going to figure out Player 1's best response quantity to each possible choice of Player 2, and then we're going to flip it around and figure out Player 2's best response quantity to each possible choice of Player 1, and then we're going to see where those coincide, where they cross.

下面我们就需要表示出,参与人1对于2不同产量下的最佳产量,然后反过来写出,在参与人1的不同产量下,参与人2的最佳产量,然后再来看看这两者在哪里相交

耶鲁公开课 - 博弈论课程节选

So, in particular, I want to figure out what is Player I's best response to each possible choice of Player II?

下面,我想知道怎样计算,参与人I,在参与人II每个策略下的最佳对策呢

耶鲁公开课 - 博弈论课程节选

So for each possible choice of S2, I'm going to draw Player I's best response and we'll do it in red.

对于任意定义域内的S2,我用红色来表示参与人I的最佳对策

耶鲁公开课 - 博弈论课程节选

For each q2 that you give me or that Player 2 chooses, I want to find out and draw what is Player 1's best response.

对与参与人2的每个策略q2,我想知道参与人1的最佳对策是什么

耶鲁公开课 - 博弈论课程节选

What is Player I's best response for each possible choice S2 of Player II?

每个s2下参与人I的最佳对策是什么

耶鲁公开课 - 博弈论课程节选

So what I need to do then is I need to figure out what is Player 1's best response for each possible choice q2 of Player 2.

所以我们要先找出,在参与人2的每个可选策略q2下,参与人1的最佳产量

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So more succinctly, Player I and Player II, at this point where the lines cross, Player I and Player II are playing a best response to each other.

简单来说,参与人I和参与人II,在这两条线的交点处,互相都采用的是最佳对策

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Okay, now I found out what PlayerIi's best response is to Player II, and what Player II's best response is to Player I for each possible choice of Player II up here, and for each possible choice of Player I down there.

好了,我们已经找到了参与人I,和参与人II互相的最佳对策了,这些是在参与人II有上面的可能策略,同时参与人I有下面的可能策略情况下

耶鲁公开课 - 博弈论课程节选