5. Interesting cases of NE

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Industrial Organization: Strategy and Competition in Business

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National Research University Higher School of Economics

Industrial Organization: Strategy and Competition in Business

9 notes

Industrial Organization is the area of economics that studies the markets as institutions, the state of competition and strategic interaction among firms, the industrial policy and the business decisions firms make within the market framework. The course looks at the markets from three different perspectives: the economic theory, the applied business perspective and the institutional and legal perspective. The focus of the course is split equally between the economic theory and business perspective but there is a significant legal component incorporated in various topics. The course includes economic modeling, game theory, numerous real life examples and several case studies. We explore interesting topics of market organization such as negotiations, antitrust, networks, platforms, electronic markets, intellectual property, business strategies, predation, entry deterrence and many others. The basic objective of the course is to enable the student to understand the structure of markets and the nature of strategic competition. Knowledge in this course will be valuable for the students in acquiring managing and governance skills, enriching their understanding of the institutional framework of business, and improve their analytical ability in negotiations. Prerequisites: The course requires understanding of basic economic modeling, knowledge of intermediate microeconomics (especially production/cost theory), knowledge of basic concepts and methodologies of game theory, intermediate econometrics and basic calculus.

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Game theory foundations

In this lecture we will focus on the principles of strategic interaction. The most important tool to understand strategy is game theory. We will define and explain different categories of games. The ultimate goal of this lecture is to enable you to use game theory so that you can model interaction and negotiations. We will talk about equilibrium in dominant strategies, which is a non-strategic equilibrium, the Nash equilibrium and the prisoner’s dilemma. We will get acquainted with static, repeated and dynamic games. I will tell you a real story of prisoner’s dilemma and we will have an extended example on firm interaction with “Energon vs. Orange”.

4. Nash Equilibrium13:07

5. Interesting cases of NE8:19

6. The prisoner’s dilemma5:54

7. Case: The cheater’s dilemma10:22

Rencontrer les enseignants

Kosmas Marinakis
Assistant Professor
ICEF and Faculty of Economics Sciences, HSE

Now, I will show you some interesting cases of games.

Let's look at this game, Anna versus Bill.

What do you think about this game?

So, if you do if you look at the necessary under linings,

you will see that this is a very similar game to

decide what game that I showed you before.

We have to Nash equilibrium.

However, try to take the role of one of these two players.

And think what would you play if you were Anna or Bill.

Now, if I was Bill, I would think in the following way.

I would say that OK if I play up,

I can get either zero or one dollar.

But if I played down,

I will get to either zero or one million dollars.

You know what? Forget about up.

I think I will play down and this is because I value one million dollars, it's much,

much more important for me than getting one dollar. All right.

So, this kind of equilibrium we call it a focal point.

We do have two totally legitimate equilibria.

Down and left which gives one million to each,

and then up and right which gives one dollar to each.

However, I bet you that if you play this game 100 times with

100 people that they seriously think

about the game and they just don't want to kid around,

all of them will select down if they were Bill,

and left if they were Anna.

This is a focal point.

It's one of the two equilibria that we focus on this equilibrium

because it's meaning it's much more important to us.

Some games they do not have equilibrium at all.

So, we look at these game for example,

we do the underlining process that I showed you before,

and we see that now there is no single cell that no one wants to deviate from the cell.

So, what is the outcome of this game?

What is equilibrium?

Actually there is an equilibrium but this equilibrium is not in pure strategies.

A pure strategy for player two, let's say,

would be either to play C or to play D. However, when you play,

for example, rock-scissors-paper, you do not say,

"I will always be playing rock."

You never say that. You say,

"I think I should play one-third of the times rock,

and one-third of the time scissor,

and one-third of the times paper."

This would be the best way to go since this is a random game.

But probably the same would be true here.

So, we can select an appropriate mixture of strategies and that mixture will depend on

the payoffs that will maximize our expected payoff in the end of the game.

How do we do that? By assigning a probability to each known dominated action.

If you have a dominated action,

you throw it out of the game and you don't bother with it anymore.

You take all your non-dominated actions here, C and D,

and A and B are non-dominated,

and then you assign a probability to each one of them.

How did you assign the probability?

In this game, you would assign a 50/50 percent probability of playing C or D,

or A or B according to which player you are because the payoffs are symmetric.

If the payoffs are not symmetric so, for example,

you had 0,2 1,0 1,0 0,1,

then in this case,

you would want to change the probabilities appropriately

and for how to derive this precisely you can go to

the textbook at page 225 and you will see how Church and Ware shows you

another nice way in order to calculate the exact mixed strategies equilibria.

What if you have no equilibrium at all?

No pure strategies equilibrium,

no mixed strategies equilibrium.

Well, you're in luck because John Nash proved

the theory in which says that for any game with a finite number of players,

which each player has a finite number of set of strategies,

then there exists at least one Nash Equilibrium either in pure or in mix strategies.

You can never have a zero Nash equilibria in a game.

You can always mix in a specific way and you will get

the situation a mixture from which no one wants to deviate from.

Let me show you now a slightly different case,

the case with incompleteness,

a case in which you do not know the full matrix of payoff. Consider this.

You're player one, you're the red person and you play player two.

Player two can play left and middle, you know that.

And you can play up and center and down.

And you know according to what player two plays,

you know how each of your strategies is going to reward you.

But you don't know the payoffs of your opponent.

How are you going to play this game?

Well first of all, if you have no information for player two,

you might think on the following way which I

warn you is not correct but you may think like that.

You say listen if I play down for sure no matter what I get one.

If I play up or center.

I risk. I may end up with three or I may end up with zero and

which one of the two will come up depends on

the other player which I don't know how the other player will play.

So, what do I want a random outcome between three or zero,

or a sure outcome of one?

Lots of people will say that this depends on your risk attitude,

how you see risk.

But we said from the very beginning

that risk attitude is not relevant in game by matrices.

Why? Because this attitude is already embodied in this payoffs.

So, we're looking to maximize the expected payoff.

So, how should you handle the incomplete game?

You should either pick down or

your alternative would be to pick a mix of 50/50 between up and center.

If you play down, you will get an expected payoff of one.

You will get for sure one actually and if

you play a mixture of 50/50 between up and center,

you will get three plus zero over two.

This would give you one and a half.

Since you have no risk attitude here,

you behave as if you were risk averse.

You prefer a mixture of up and center by 50/50 rather than playing down.

So, all we have here a very interesting case where

a mixed strategy dominates strictly a pure strategy.

So, a mixture of 50/50 between up and center dominates strictly the pure strategy down.

After this, I will show you the most famous example in game theory,

one that is extremely interesting,

and we're going to use in almost every lecture from now on. Stay with us.

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