This is a Chinese version of Competitive Strategy. You can find the original course in English from our course catalog. 此版本是Coursera首次尝试推出的中文翻译版。课程视频为英文原版附中文字幕，课程页面和测验已译成中文，帮助中心提供中文支持。 在本课程（共六个模块）中，你将了解企业在战略决策相互依存的情况下如何行事。例如，你的行动会如何影响竞争对手的利润，反之亦然。我们将会借助博弈论的基本工具分析企业如何选择策略以获得竞争优势。
纳什均衡 Nash Equilibrium
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Del curso dictado por Ludwig-Maximilians-Universität München (LMU)
竞争策略（中文版）
423 calificaciones
De la lección
关注你的竞争对手 Take Care of Your Competitors
在本模块中，我们将介绍博弈论的基本概念，并分析策略博弈中的竞争情况。我们将明确什么是策略并寻求不同的方式来确定最佳策略或优势策略。我们还将讨论纳什均衡和囚徒困境概念，分析为什么在决策时考量其他局中人的行动至关重要。最后，我们还将分析同时博弈（所有人同时行动）更改为序贯博弈（局中人按序行动）时会出现的情况。
Conoce a los instructores
Tobias KretschmerProfessor
Institute for Strategy, Technology and Organization
So hello back. Great to have you here, and hope you
enjoyed the pizza. In this video, we'll introduce the idea
of the Nash Equilibrium, which is a more formal and precise way of thinking about
optimal strategies. And to do that, let's go back to the
example of the Piccola Osteria and Pizza Rosso, which both sell pizzas to students
around the university, here in Munich. And we'll look at the simplified version
of this game, where we already eliminated the dominated strategies of charging a
low price for both of these players. Okay, so in the simplified version in the
last video we saw that really somehow, it seems to be the best thing, the best
strategy for both, to charge a medium price.
But what is it that we actually did when we looked for the best price, the optimum
price? Well, we looked for a Nash
Equilibrium. But what is a Nash Equilibrium?
A Nash Equilibrium is a combination of strategies such that no player can
deviate unilaterally from his or her strategy.
To do what? To improve his or her payoffs.
And so indeed, once we found a Nash Equilibrium, we found a sort of a natural
resting point of the game. Because no player wants to do something
else, assuming that the other player sticks to his or her strategy.
And to do that a little bit more practically, to try to find out what this
actually means in practice, let's go back to the game that we just looked at.
Okay, so we've got the two players. We've got Pizza Rosso and Piccola Osteria
and both of them can choose between a high and a medium price.
So, if for example, Piccola Osteria charges a high price, what's Pizza
Rosso's best strategy? Their best strategy is to charge a medium
price because seven thousand is more than six thousand.
On the other hand, if Piccola Osteria charges a medium price, then it's best
for Pizza Rosso, again, to charge a medium price.
And we can do the same thing for Piccola Osteria, so if Pizza Rosso charges a high
price, then Osteria will charge medium. And if Pizza Rosso charges a medium
price, then it's best for the Osteria to charge a medium price again.
So what we have is a situation where both players, Osteria and Rosso charge a
medium price and that's their optimal strategy.
So lets look at this from the perspective of a Nash Equilibrium.
Does any of the players have an incentive to deviate from the current strategy?
Okay, so let's assume that Piccola Osteria play their strategies, so they
play medium price. What's best for Pizza Rosso?
Well Pizza Rosso won't want to change from a medium price to a high price
because it would lower their profits. And by the same token Osteria would not
want to change price if Pizza Rosso charges a medium price.
Okay? So for them, it's best again to stick to
the price that they had in the Nash Equilibrium.
So now, it's actually your turn. And have a look at this short game and
try to find out what the Nash Equilibrium is.
I'll see you in a second.
Great, so now you've had a bit of practice. Let's try and put the Nash Equilibrium
into perspective with another couple of concepts that we have already learned in
the course. So let's just ask a couple of questions.
So, first, is a Nash Equilibrium the same as a dominant strategy?
Second, can a Nash Equilibrium contain dominated strategies?
And, third, will every Nash Equilibrium contain dominant strategies?
Okay, so these are the concepts that so far
we've studied in the course. Let's now put these things into
perspective. Is a Nash Equilibrium the same as a
dominant strategy? It's not.
Why? Because a dominant strategy refers to a
single player, a Nash Equilibrium, as we know from the definition, is the
combination of strategies. It's a strategy for each player in the
game. Can a Nash Equilibrium contain dominated
strategies? Well, let's think back to what a
dominated strategy actually is. It's a strategy for which you have
another one that always does better. Okay?
So if we want to maximize our profits, if we want to maximize our payoffs,
we're going to choose something that will give us the highest payoff.
So a dominated strategy will never be part of a Nash Equilibrium.
And finally, will every Nash Equilibrium contain dominant strategies?
Well, no, as we'll see in a second. So let's go back to the full version of
the of the pizza war and let's have a look.
Well, what we know is that here, the Piccola Osteria will never
charge low prices. That's a dominated strategy, and of course
it can't be part of the Nash Equilibrium. By the same token, Pizza Rosso cannot do
that. However, what we found is that neither
Pizza Rosso nor the Osteria has a dominant strategy.
And let's have a look at how we find this, okay?
What is a dominant strategy? A dominant strategy is one that does
better than any other strategy regardless of what the other player does.
Let's go through this. If Piccola Osteria charges a high price
the best strategy for Pizza Rosso is to charge medium.
If Piccola Osteria charges a medium price, the best strategy is to charge medium.
But, if Piccola Osteria charges a low price, then the best strategy for Pizza
Rosso is actually, to charge a high price.
So, by that definition, Pizza Rosso does not have a dominant strategy because
there's no strategy that always does better than the other one, okay?
And we can do the same for Piccola Osteria, and we find that here the best
responses, again, are not necessarily just one strategy.
So we can have a Nash Equilibrium that's just one without any player having a
dominant strategy. Okay?
So that's just throwing these concepts around and trying to put them into
perspective. Let's go a bit further into the concept
of a Nash Equilibrium and see what the nature of a Nash Equilibrium is.
So will every game have a Nash Equilibrium in pure strategies.
In other words, will there always be a combination of one behavior of one player
and one behavior of the other player that is a natural resting point of the game?
And for that, let's take a look at one of my favorite sports football, or soccer.
Okay, and of course one of the most exciting points in a game is when
there's a penalty, okay? So we've got a penalty taker, and we've
got a goalie, and of course each one wants to win.
So to simplify height of the shot and so on lets just assume there's left
and right. Okay, the goalie can either dive to the
left or to the right and the penalty taker can either shoot to the left or to
the right. So if they both end up in the left side
of the goal, meaning that the goalie jumps to the left and the penalty taker
shoots to the left. Then the goalie wins, he catches the
ball. If the goalie goes to the left, the
penalty taker goes to the right, then the penalty taker wins, because he scores the
goal. And by the same token, whenever you have
both goalie and penalty taker jumping or shooting to the same side of the goal the
goalie wins. If its opposite sides the shooter wins.
Now what's interesting about this game is that there is never a situation where
price. Okay?
It's either the goalie winning or it's the penalty taker winning.
So that means that we never have a stable situation.
We don't have a natural resting point of the game.
So the second question is, can a game have more than one Nash Equilibrium.
In every game that we've looked at so far, we had either no equilibrium, in the
case of penalty taking or we had one equilibrium, as in the game of
Pizza. Okay.
So can there be a situation where we have multiple Nash Equilibria?
So as an example here we can think of the battle for competing technical standards.
So we have firm A and firm B, both of them have developed a standard, Standard A or
Standard B. And they both want to choose one of these
two technologies. If you look at the payoffs here, what
you'll find is that there are two Nash Equilibria.
Okay. So, if Firm B chooses Standard A, Firm A,
of course, wants to choose Standard A as well.
And if firm A chooses standard A, then it's best for firm B to also choose
standard A. So we have one Nash Equilibrium here.
At the same time, if firm A chooses standard B, then of course firm B will
want to choose standard B as well. Because that gives them a higher payoff
and by the same token if B chooses their own standards, standard B,
then Firm A will want to follow and also choose standard B.
So here we are faced with a situation of two Nash Equilibria.
Okay? So, for example one of the
real life cases that was looking at precisely such a situation was Sony and
Phillips. When they started developing the compact
disc in the late 1970s and early 80s, both of them knew they wanted to
standardize, but it was difficult to see which of the two standards was going to
be chosen. Sony, of course, wanted to get as much as
possible of their own standard into the system.
Phillips wanted to build as much of their own system into the standard.
In the end they ended with a sort of combination of both and were very
successful. So the CD was one of the most successful
introductions in consumer electronics. So we've just learned about the Nash
Equilibrium as the natural resting point of the game.
So at this point, in a Nash Equilibrium, no player can gain higher payoffs by
playing another strategy. So, in a competitive situation, we would
expect two rational rivals to choose their strategies such that they will end
up in a Nash Equilibrium. So, of course, in some situations, there
may be no Nash Equilibrium at all, as we've seen in the game of football and
soccer. In other settings, we have two or even
more Nash Equilibria. So, what's interesting there is that, how
do we select? How do we solve these sorts of games?
So in the next video, we'll have a closer look at these kinds of games.
But first, do have a look at the following game, and put down how many
Nash Equilibria there are.
Okay? Thanks very much, and see you very soon.
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