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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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