Once you delete the dominated strategies, then you kind of go through it again and then 2 is dominated by 3.

一旦你剔除了劣势策略,再次审视这个博弈时,立场2劣势于立场3

耶鲁公开课 - 博弈论课程节选

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

So both the investment game and the game with... the partnership firm game are games with strategic complements.

投资博弈以及合伙人博弈,都是策略互补博弈

耶鲁公开课 - 博弈论课程节选

These games in which the more the other person does the more I want to do, these are called games of strategic complements.

这种别人付出越多,你就付出越多的博弈,叫做策略互补博弈

耶鲁公开课 - 博弈论课程节选

So these strategies -- let's be careful here with the word weakly here -- these strategies are not weakly dominated in the original game.

所以这些策略,对于这里的弱一词,我们要谨慎对待,这些策略在原博弈中并不是弱劣势的

耶鲁公开课 - 博弈论课程节选

So we know that all the numbers between 45 and 30, these strategies were not dominated.

所以可知选择30至45之间的数,这样的策略在原博弈中并不是劣势的

耶鲁公开课 - 博弈论课程节选

Every game we've seen in the class so far has had a discrete number of strategies.

目前为止我们遇到的博弈,每个策略都是不连续的

耶鲁公开课 - 博弈论课程节选

But they are dominated once we deleted not just the dominated strategies, but also the strategies that were dominated once we deleted the dominated strategies.

但是当我们我们,剔除原博弈中的劣势策略以及,第一次剔除之后仍处于劣势的策略后,它们就又继续成为了劣势策略

耶鲁公开课 - 博弈论课程节选

The strategies that are less than 67 but bigger than 45, I think these strategies are not, they're not dominated strategies in the original game.

对于选择大于45而小于67的数,我认为他们并不是,在原博弈中并不是劣势策略

耶鲁公开课 - 博弈论课程节选

So much for talking about coordination games and helping you with your dating strategy.

讲了有关协调博弈和约会策略的问题,今天我们就讲这么多了吧

耶鲁公开课 - 博弈论课程节选

Strategic substitutes is a strategy, is a statement about the nature of the game.

策略替代是一种策略,这是对于博弈性质的一种描述

耶鲁公开课 - 博弈论课程节选

So this game is a game, not of strategic complements, but of strategic substitutes.

这不是一个策略互补博弈,而是策略替代博弈

耶鲁公开课 - 博弈论课程节选

So we've now got all of the ingredients of the game: players, strategies, payoffs.

现在这个博弈的所有要素都有了,参与人,策略和收益

耶鲁公开课 - 博弈论课程节选

The reason I don't want to play a strictly dominated strategy is, if instead, I play the strategy that dominates it, I do better in every case.

我不选择严格劣势策略的原因是,要我选了优势策略,我在每次博弈都得到更好的收益

耶鲁公开课 - 博弈论课程节选

Notice this game is not symmetric in the payoffs or in the strategies.

但注意此博弈的策略与收益是非对称的

耶鲁公开课 - 博弈论课程节选

Delete those. Look at the game with all those dominated strategies deleted.

先剔除劣势策略,然后重新观察这个博弈

耶鲁公开课 - 博弈论课程节选

The main textbook is this one, Dutta's book Strategy and Games.

主要是这本,杜塔的《策略与博弈》

耶鲁公开课 - 博弈论课程节选

We also saw in that numbers game last time that in some games, but by no means all games, in some games this process actually converges to a single choice.

我们同样可以发现,在某些博弈中,不是所有的博弈,迭代剔除劣势策略,最终会导致唯一的选择

耶鲁公开课 - 博弈论课程节选

Game Theory is a method of studying strategic situations.

博弈论研究策略形势

耶鲁公开课 - 博弈论课程节选

Second ingredient of the game are strategies.

博弈的第二个要素是策略

耶鲁公开课 - 博弈论课程节选

These are games of strategic complements.

这些都是策略互补博弈

耶鲁公开课 - 博弈论课程节选

And underlining what arises in this game, notice that in this game we're able to eliminate one of the strategies, in this case the strategy of shooting to the middle, even though nothing was dominated.

我们从这个博弈中可以得出,我们能够剔除其中的一个策略,在本案例中是从中路射门,尽管这里并没有劣势策略

耶鲁公开课 - 博弈论课程节选

So the players in this game are two firms and the strategies in this game for the firms and this is going to turn out to be important the strategies are the quantities that they produce of an identical product.

这个博弈的参与人是两家公司,他们的可选策略如下,以后你会知道这是多么重要,策略是,某种同质商品的产量

耶鲁公开课 - 博弈论课程节选

Why is it that when we see these law partners, or medical partners, or whatever it happens to be, or students together on a homework assignment, why is it we tend to get inefficiently little effort when we start figuring out the strategy and working through the game?

为什么这些律师事务所的律师,医疗合伙人或者其他类似的机构,还有一起做作业的学生,当我们研究过这些策略和博弈后,为何这样的组合往往是收效甚微的

耶鲁公开课 - 博弈论课程节选

So now we've ruled out the possibility that anyone's going to choose a strategy 68 and above because they're weakly dominated, and we've ruled out the possibility that anyone's going to choose a strategy between 46 and 67, because those strategies are dominated, once we've ruled out the dominated strategies.

现在因为选择68,及以上的数的策略是弱劣势策略,所以我们已经把它们剔除了,并且我们也排除了有人会,选择46至67之间的数的可能,因为一旦我们剔除原博弈的劣势策略,这些策略也就变成劣势策略了

耶鲁公开课 - 博弈论课程节选

Okay, so if we had stopped the class after the first week where all we learned to do was to delete dominated strategies, we'd be stuck, we'd have nothing to say about this game and as I said before, this is the most important game, so that would be bad news for Game Theory.

好了,如果我们只学了第一周的内容,即如果我们只学到了剔除劣势策略的话,我们没招了,我们无法解释这个博弈,但我之前说了,这是个很重要的博弈,这对博弈论来说可不是个好消息

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