So hello again. You ready for more? 所以你好你准备好了吗?
In the previous video we've looked at a very simplified version of the Diamond 在前面的视频我们看了一个 非常简化的版本的钻石
Cartel. We've had South Africa and Australia as 卡特尔。 我们有南非和澳大利亚
the only two players in this game. And we said okay, well they repeat to set 唯一的两名竞争者在这场博弈。 和我们说过的,他们重复设置
prices or they repeat setting prices or quantities forever. 价格或重复设置价格或 数量永远的。
But there's a likelihood of P that there's going to be a market in the next 但是有一个可能性,P 将会有一个市场在未来
period, right? So that was all we looked at in 期间,对吗? 所以这是我们看到的
this in previous video. But, reality of course is going to 这在以前的视频。 但是,现实当然是去
look slightly different because there are other factors that may affect 看起来有些不同,因为 还有一些其它因素可以影响
the likelihood of cooperation. So in this video we'll look at precisely 合作的可能性。 所以在这个视频我们将看看精确
that. So just to recap, each country in our 所以只是回顾一下,每个国家在我们的
previous model would cooperate this year if the payoff from cooperating is higher 之前的模型将今年合作 如果回报更高的合作
than the payoff from deviating. So, the payoff from cooperating, just to 大于偏差。 所以,回报的合作,
recap, it's half the monopoly profit, that's what you get each period. 总的来说,它的一半的垄断 利润,这是你们应得的每个时期。
And if you just continue doing that until the market disappears, the overall value 如果你继续这样做,直到 市场消失,整体的价值
of this is going to be 1 divided by 1 minus p. 这将会是1除以1 - p。
The payoff from deviating is $49 million, because you only get this deviating 的回报,出轨是4900万美元, 因为你只得到这个出轨
payoff once. And after that, it's going to be 收益一次 和之后,这将是
competition forever. Of course we know that p is the 永远的竞争。 当然我们知道,p是
probability that the game goes on, and if p is a small number, 概率游戏继续,如果 p是一个小数目,
so if p is very close to zero, then this would mean that this number, this goes 所以如果p是非常接近于零,那么这个 意味着这个数字,这是
close to one, and therefore this gets close to 25 million, 50 million divided 接近一,因此这得到 接近2500万分开
by 2. So it's less likely that we'll cooperate 除以2。 所以这是不太可能,我们会合作的
if the likelihood that the game goes on is very small. 如果可能,竞争继续 是非常小的。
On the other hand, if p is close to 1, this is going to be very close to zero. 另一方面,如果p是接近1, 这将是非常接近于零。
This is going to mean that this will become very large, and therefore this 这将意味着这将 变得非常大,因此这
overall payoff from cooperating will become very large. 总体回报的合作将 变得非常大。
So if the likelihood that the market is going to continue is high, 所以如果可能,市场 要继续高,
then we're likely to cooperate But, this is really not the only thing 然后我们可能合作 但是,这是真的不是唯一的东西
that will play a role in determing if we want to cooperate or not. 将扮演一个角色在决定如果我们 想合作或不是。
So one thing that will play a role is the number of competitors. 所以一件事情将会扮演一个作用是 竞争对手的数量。
So we've looked at South Africa and Australia as the only two diamond 所以我们看了南非和 澳大利亚是唯一两个钻石
producing countries. That's not realistic, there's more 生产国家。 那是不现实的,还有更多
countries that produce diamonds, and that may be part of this cartel. 国家生产钻石, 可能这部分卡特尔。
So, if there are more competitors, that's going to mean that the share of the 所以,如果有更多的竞争对手,这是 将意味着分享的
monopoly profit that I get as a participant in this cartel gets smaller. 垄断利润,我得到一个 参与者在这个卡特尔变小
So here, we've had the payoffs from cooperating were monopoly profits divided 所以在这里,我们有回报。从 合作是垄断利润划分
by 2 i.e., South Africa got half of the profits and Australia got a half of the 除以2 i.e.。,南非有一半的 利润和澳大利亚有一半的
profits. Now if there are ten players, ten 利润。 现在如果有十个竞争者,十
countries producing diamonds, then this number will be replaced by ten. 国家生产钻石,那么这个 号码将被替换为10。
So this means that our payoff per period, from being part of the cooperative 所以这意味着我们的回报/期, 从部分的合作
agreement, is going to be much smaller. And I'm less likely to cooperate, okay? 协议,将会小得多。 和我不太可能合作,好吗
I still have the same potential payoff from deviating, but my payoff from 我仍然有相同的潜在回报 从出轨,但我的
cooperating decreases. Another aspect is the importance of the 降低合作。 另一个方面是重要的
future. So how important do I value the future? 未来的。 所以我要多重要价值未来?
If the future becomes more important, the interest rate, where this is usually 如果未来变得越来越重要, 利率,这通常是
reflected by a decrease in the interest rate. 反映在降低利息率。
So let's do a quick thought experiment. if the interest rate would be very high, 所以让我们做一个快速的思维实验。 如果利率将是非常高的,
then the difference that I assign to an amount of money that I get today and an 然后,我分配给一个不同 多的钱,这是我今天得到和一个
amount of money that I get tomorrow is going to be very strong, is going to be 多的钱,这是我得到明天 将是非常强大的,将会是
very large. Because I could reinvest the money that I 非常大的。 因为我可以再投资钱我
get today for one period, and that would give me a very high return. 今天得到一期,将 给我一个非常高的回报。
So that means that if I assign a high value to the future, that means it's 这意味着,如果我分配一个高 价值未来,这意味着它的
almost worth as much to me as the payoff today. 我几乎金额作为回报 今天。
So this is going to mean that if I have a low interest rate, then payoffs today and 所以这将意味着,如果我有一个 低利率,那么今天,回报
payoffs tomorrow are almost the same size. 明天是几乎相同的回报 大小。
So this is going to change our payoffs from cooperating. 所以这将改变我们的成果 从合作
And it's going to change it by adding this additional formula. 和它将改变它通过添加 这额外的公式。
So if we just play this through for a second, if the interest rate is small 所以,如果我们只是竞争这种通过 第二,种如果利率很小
this is going to be close to 1, this here is going to be close to zero. 这将是接近1,这这里 将接近于零。
This is going to become very large, and therefore this whole expression is going 这将变得非常大, 因此这整个表达式会
to become very large. So a small interest rate is going to make 变得非常大。 所以一个小的利率会使
it more likely that I'm going to cooperate. 更有可能我要去合作
Another possible influencing factor is the degree of punishment. 另一个可能的影响因素 惩罚的程度。
Remember what we played before? 记得我们之前的竞争吗
The agreement was I'm going to cooperate, but the moment you don't cooperate I will 该协议是我要合作, 但当你不配合我
punish you very hard. So I will go down and charge low prices 惩罚你更加艰难。 所以我将继续下降,费用较低的价格
forever. This is what's called the trigger 永远的。 这就是所谓的触发器
strategy the moment you pull the trigger, there's never going to be cooperation any 策略当你扣动扳机, 永远不会有任何合作
more. It's a very harsh punishment. 更多的。 这是一个非常严厉的惩罚。
And let's see what happens if we make this degree of punishment a little bit 让我们看看会发生什么,如果我们做 这种程度的处罚有点
softer. So we change the agreement to say well as 柔和的。 所以我们改变协议说也
soon as one country charges a low price in one year, the other one will charge 一旦一个国家收取低价格 在一年,另一个会收取
low prices for the next five years. So it's only a limited period of time 低价格在接下来的五年。 所以这只是一个有限的时间
that we punish the other player, the player that didn't cooperate. 我们惩罚其他竞争者 不配合的。
So the payoff from cooperating is not going to change, right? 所以回报的合作不 要改变,对吗?
Because that's the path where we never have to use the punishment. 因为我们从来没有路径 必须使用惩罚。
On the other hand the payoff from deviating does change. 另一方面的 出轨并改变。
So we get the 49 million from cheating once, we get 0 profits for five periods, 所以我们得到4900万从作弊 一次,我们得到0利润对于第五阶段
but then after that we get 50 million divided by 2. 但是,我们得到5000万之后 除以2
Because we revert back to monopoly prices and we share the monopoly profits. 因为我们回复到垄断价格 和我们分享垄断利润。
So this means that I have to take this into account that maybe the market isn't 所以这意味着我不得不把这 考虑,也许市场不是
going to exist by then. But if it does then we start reverting 要存在,然后。 但如果它这么做我们开始恢复
back to monopoly prices after these punishment periods of five. 回到垄断价格在这些 处罚时间的五个。
Okay, so to sum up, we found what some of the factors enhancing cooperation are. 好吧,总而言之,我们发现了一些 加强合作的因素。
In particular we looked at the importance of future payoffs. 特别是我们看着的重要性 未来的回报。
If I value the future highly, then it's more likely to behave cooperatively in 如果我珍惜未来的高度,那么它的 更容易表现在合作
the present. We also identified some factors that make 目前的。 我们还发现了一些因素,使
cooperation more difficult. In particular if we are in the market 合作更加困难。 特别是如果我们在市场
with a large number of competitors, it's more difficult to maintain cooperation. 与大量的竞争者,它的 更难以保持合作。
Where does that come from? Comes from the fact that if we have to 来自哪里? 来自一个事实,即如果我们必须
split the profit from cooperation over a large number of 从合作中分得利润 在大量的
players, then each individual player will get 竞争者, 然后每个玩家都会得到
a smaller piece of the pie, and he's more Inclined to deviate. 一个较小的一块蛋糕,和他的更多 倾向于偏离。
The low degree of punishment, or a forgiving punishment, also makes 低程度的惩罚,或一个 宽容的惩罚,也使
cooperation more difficult. Now that's quite interesting because if 合作更加困难。 现在,很有趣,因为如果
you have a very draconian punishment, like the trigger strategy, 你有一个非常严厉的惩罚, 如触发策略,
the moment you misbehave I'm going to start punishing you 当你表现不好我要 开始惩罚你
forever, okay? That draconian punishment is actually 永远,好吗? 这严厉的惩罚实际上是
very good for cooperation, because people are deterred by this punishment. 很好的合作,因为人们 正因这个惩罚
Okay, so to sum up, we've basically built up a a model of cooperation in a 好了,总之,我们已经基本建立 一个一个的合作模式,在一个
prisoner's dilemma and we found that in a finitely 囚徒困境 我们发现,在一个有限
repeated game, cooperation is very unlikely. 重复博弈中,合作是非常 不太可能。
Because we just look at the endpoint of the game, and we solve the endpoint by 因为我们只是看看的端点 竞争,我们解决端点通过
moving the game forward. On the other hand, an infinitely repeated 向前移动竞争。 另一方面,一个无限次重复
game can give us cooperation under certain circumstances. 游戏能给我们下的合作 某些情况下
And these circumstances are basically affected by a number of structural 而这些情况基本上是 受到一系列结构
parameters in the market. Instructional parameters like the 参数的市场。 教学参数如
likelihood of future payoffs, the importance of future payoffs, the number 未来可能的成果, 未来回报的重要性,这个数字
of competitors and the degree of punishment. 竞争对手和程度的 惩罚
So with that I hope that we brought that model, that seemingly abstract model of 所以,我希望我们把它 模型,模型的抽象
cooperation a little bit closer into reality. 合作有点接近 现实。
And look forward to seeing you in future sessions. 和期待看到你在 未来的会议。
Thanks. 谢谢。