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No, they didn't. Not initially at any rate, but notice as we played the game repeatedly, what happens?
我觉得绝对没有人会,但是注意下如果我们重复博弈会怎样呢
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so we got to originate the parts that we played.
所以我们要加紧创作我们自己的那部分。
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So in that game we played at the end last time, what were the set of strategies?
上节课我们最后做的游戏,策略的集合是什么样的呢
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We played that game last time, right?
我们之前这样做过，对不？
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When we looked at the random walk series I think the representativeness heuristic played a role in there as well.
当我们观察随机漫步序列时,我认为代表性原则偏误,也起了一定作用
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What we've done is taken this pitch and played it all the way down an octave below it so we're actually getting back to this configuration of the pitch right next to it, and we could--then of course we could go down one more step and we would get the octave, which is a duplication of two-to-one.
我们所做的是固定一个音高，向下一路弹奏一个八度,所以事实上我们又回到了与这个固定音高相邻的音上，我们当然也可以向下再弹一组，然后得到这个八度，这其实就是两个八度对一个八度的重复。
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so we in return like played them a song.
所以，作为回报，我们为他们弹奏了一曲。
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So many of them would have gone up to Jerusalem and a real tension is going to develop between the Jerusalem priests and this class of Levites who are newcomers; and we'll see some of that tension played out in some other texts.
他们中的许多人将去耶路撒冷，一次真正的紧张状态,将在耶路撒冷的牧师和这些新来的利未人,中逐渐发展起来;我们将会在其它的经文中,看到一些这种紧张状态。
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As we played the game repeatedly, we noticed that play seemed to converge down towards 1.
当我们不断地重复博弈,我们会发现最后会不断接近1
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We're going to ask for the same grade game we played at the beginning.
我们来求成绩博弈在此情况下的结果
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Let's go back to the game we played with the numbers.
那我们回到之前玩的数字游戏
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One other remark before we leave this, in the game we played last time, in the investment game, one feature of that game was that the more you thought other people were going to invest, the more you wanted to invest.
在继续讲下面的内容前,我再多说几句,上一讲的投资博弈有一个特征,就是如果你越认为大家会投资,你就越想投资
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We played a game at the very end last time, where each of you chose a number - all of you chose a number - and we said the winner was going to be the person who gets closest to two-thirds of the average in the class.
我们在上节课最后做了一个游戏,你们每个人都选了一个数字,你们所有的人都选择了一个数字,选择的数字最接近全班,平均数的三分之二的人就是赢家
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So far we've looked at this game as played by people and we've looked at this game who are evil gits, as played by people who are indignant angels.
目前为止我们对这个博弈的分析,还停留在局中人都是饭桶恶魔,或者都是愤怒天使的阶段呢
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Okay, so last time we looked at and played this game.
上节课我们做了这样一个游戏
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The game I just put up, that's a trivial example, it didn't really matter which equilibrium we played here, we just wanted to play an equilibrium, is that right?
但是现在讨论的这个小案例呢,到底达成哪个均衡并不重要,重要的是我们要达成均衡,是这样吧
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We've played it three times, Let's try and figure out what the equilibria looked like in this game.
我们做了三次,我们试着解决,此博弈中的均衡是什么样子
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We did something very nerdy, namely, we just played with calculus and algebra.
我们使用了些死板的,微积分和代数
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So we were able to dominate 1 and 10 in the first round, so we know this won't be played, and we know this won't be played.
在第一次推理中1和10是劣势策略,我们知道无人会采用它们,我们就不会去采用它们
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Now how do we think this game is going to be played?
下面来看看这次博弈讲如何进行的
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But if we played this game up in let's say the Divinity School, I'm guessing that Travis' answer is reflecting what you guys are reasoning here.
但是我们要是在神学院做此博弈,我猜特拉维斯的回答,反映了你们的理由
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- And lastly, you might have recalled the Fruit-craft RPG game that we played briefly with the little man that moves up and down, left and right and collects like oranges and apples and then brings them into the store.
最后，我需要你们回想一下之前玩过的一个游戏,“Fruit-craft，RPG“，我们只需要让那个小人,上上下下，左左右右地移动，收集桔子啊，苹果啊等等,然后把它们送到仓库里去。
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Did people play Nash Equilibrium when we played that game?
谁在做这个游戏时就想到纳什均衡了吗
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For example, if we played this game up in the business school-- are there any MBA students here today? One or two.
假如我们要在商学院进行这个博弈,这里有念MBA的吗,有一两个
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I'm going to see if I have enough money to do this in class When we played this game in the old days, during the dot com boom with the MBA students, you had to put fifty dollars on the table to get them interested.
我看看我有没有足够的现金,在之前和MBA学生做这个游戏的时候,那时候正赶上互联网大繁荣,你得拿出来50美元他们才有兴趣
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