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So this is a classic game, perhaps it's one of the most famous games, and therefore worth studying in the class.
这是一个经典的博弈案例,可能是最著名的博弈案例之一,它很值得在我们课堂上研究一下
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I mean, obviously it's different because it's about something different, but I mean in terms of the Game Theory it's different.
很显然二者的研究对象不同,但是我是说二者涉及的博弈理论也不同
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So,after taking into account the market impact, and the commissions,and the fees, this zero-sum game becomes a negative-sum game.
所以,考虑到市场冲击,佣金,规费,这一零和博弈变成了负和博弈
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So a hundred years really before the invention of Game Theory, someone had figured out this answer for this game.
一百多年前博弈论还没有诞生呢,那时就有人解除了这个博弈的答案
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Even though these best responses are pretty complicated it turns out that there's only one Nash Equilibrium in this game.
虽然最佳对策是很复杂的,在这个博弈中却只有一个纳什均衡
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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
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You also need to put yourself into other people's shoes and think about how sophisticated are they at playing games.
你还要站在别人的立场上,思考他们在博弈时有多老练
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And in this game if they keep on doing that, it's going to drag them back to Nash Equilibrium.
这个博弈,如果他们一直这样做,最终会达到纳什均衡的状态
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Well I guess I thought we could be more collusive and kind of work together, but I guess not.
我觉得我们本可以团结合作的,但是我看在这个博弈中不行
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And perhaps, the lesson I want to draw out of this is that right now this is not a game.
我希望大家从中发现,这并不是真正意义上的博弈
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So we're going to be doing political science or political science as it meets Game Theory for the rest of the day.
我们将在今天接下来的时间学习政治科学,亦即是政治和博弈论的结合
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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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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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By the way, if this is beginning to sound like a wrestling match, I don't mean it to.
顺便说一下,我可没有把这个博弈,弄得像摔跤比赛的意思
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So I'm going to have to figure out what the odds are of that in doing this exercise.
因此在做类似的博弈前,我们需要先弄清楚收益是什么
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So this is a game, just to give you some more jargon, this is a normal-form game.
用专业术语来说,这个博弈,属于标准式的博弈
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The voters, or candidates, whatever you want to call them, depending on where they stand, in this game they're going to be you.
选民或候选人,随便你们想怎么叫,基于他们的选择,在这个博弈中他们是你们
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So for those of you--for the half of you -that are going to end up in law school, this is pretty good training.
我估计你们多数人可能会去读法学院,博弈论对你们来说是门不错的基础课
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I took the second payoff from that matrix and made it the second payoff in this matrix.
那个矩阵里面的第二个收益就是,这次博弈的矩阵里第二个收益
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Right, so you should all have been choosing in this game, you all should have chosen Alpha.
对,在这次博弈中,你们应该都选α
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But in the real world that's a sequential game, people decide to run in some order, we're going to assume this is all simultaneous.
但在现实生活中这是个有顺序的博弈,人们依照某种顺序决定是否参选,我们将假设这全是同时发生的
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It matters in how we take games through to the real world, and we're going to see more of this as the term progresses.
把博弈理论运用到实际是很重要的,本学期我们会不断学习类似的案例的
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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
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And what we're going to do today is analyze this game under both those possible payoffs.
接下来我们分别用不同收益,来分析一下这个博弈
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This game also has the feature that the more effort the other person, the more the other person does, the more you want to do.
这个博弈也有这个特征,别人越努力你就会越努力
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So this is the total quantity produced on this equilibrium, in this Cournot Nash Equilibrium.
这就是在古诺博弈中的,纳什均衡
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We have the same basic structure, the same outcomes, but we imagine people cared about different things and we end up with a very different answer.
博弈的结构,结果都一样,但是人们在乎的东西不同了,所以我们得到了完全不同的答案
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It's a good idea to try and figure out what your goals are-- what you're trying to achieve-- before you go ahead and analyze the game.
它能帮我们在分析博弈之前,先弄清我们的目的是什么
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What is it that's different about this game from the... What's the obvious thing just looking at this picture that makes it different from the partnership game.
这个博弈的不同之处在于,从这个图上能很明显看到的,它与确实与合伙人博弈有所区别
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I know this might be changing the game a little bit, but if you ever expected to play the same game with the partner you have more.
我知道这可能会稍微改变点这个博弈,但是如果你认为以后你还会,和你的对手进行相同博弈
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