Video tutorial: Coordination game - YouTube

4.13, social interactions and conflict in the choice among Nash

equilibria. In this section I present to you another

game: the players are the same, Bala and Anil,

they're making a decision about producing cassava

and rice and they are making this decision at the same time.

They cannot communicate with each other while making this decision.

Now, as before, in order to find out if this game has any Nash equilibrium we

need to put ourselves in the shoes of each player and analyze the game.

I'm now inside Anil's head, I'm Anil now. What am I going to do if Bala decides to

produce rice? If I produce cassava I'll get four, for rice

I'll get zero, so producing cassava is my best response if Bala produces rice.

I put a dot here to mark my

best response, Anil's best response in this case.

What if Bala decides to produce cassava? If I produce rice I'll get two, if I

produce cassava I'll get one so my best response in this

case is to produce rice and I'll put a dot here to represent

my decision and his best response in that case.

Now let's get out of Anil's head and go inside Bala's head. I am now Bala.

What am I going to do if Anil decides to produce

cassava? Now in this case if I produce cassava I'll get zero, for rice

I'll get four, therefore I decide to produce

rice and I put a circle around that decision to mark my

best response, Bala's best response.

Now what if Anil decides to produce rice? What would be my best strategy? If I

produce cassava, I'll get two, for rice I'll get one, so

cassava is my best strategy, and then I'll put a circle around

that strategy to represent my best response,

Bala's response. Now let's take a step back and look at the game from a

perspective of an outsider. We realize three things:

first, that this game has two Nash equilibria.

The best response of both players meet with each other

in these two cells so that's the first thing;

the second thing is that if we focus on these two Nash equilibria

both of these are better than the other two cells.

What does this mean? It means that both players

are better off as long as they don't compete with each other,

as long as they don't produce the same thing;

and finally if you look at these two equilibria we

realize that one of them is inferior to the other one,

and in reality people might get stuck in that equilibrium. That

equilibrium can persist, why? Because remember, these two

players cannot coordinate their decision with each other, they cannot communicate.

Let's assume Bala is producing cassava, then Anil has to produce rice,

there is no point in Anil producing cassava as long as

Bala is not switching to rice.

However in reality players can end up in this better equilibrium on the

basis of expectation. Let's say Anil expects Bala

to produce rice, why? Because you know generation

after generation people have been producing

rice in Bala's district so on the basis of this expectation

Anil produces cassava and both these players

end up in the better equilibrium without talking with each other.

Well you might say to yourself, what does this all have to do with the real world?

In real world you know Bala and Anil can talk with each other

and coordinate their decision and end up here.

Well that's not necessarily the case. If we increase the number of players in the

game in the real world you know businesses

and households, a lot of them have to make a decision

at the same time and it's not always easy for them to get inside one room and

coordinate their decisions, and because of that sometimes the firms

in one industry can get stuck in an inferior equilibrium,

and in order to get out of that equilibrium they need an outside

intervention by the government. Let me give you an example: let's think

about the barcode technology. That's one of the most

important innovations of 20th century that dramatically increased the

productivity of the supermarkets in the retail sector.

But it took many many years for the supermarkets

and the producers of the goods to adopt this technology of barcode,

why? Because of all these coordination difficulties.

Let's see this issue from the perspective of producers of goods.

Let's say I'm a producer of cornflakes. I would

adopt the barcode technology only if the supermarkets that I'm selling my

cornflakes to move to this technology as well.

Now let's see it from the perspective of supermarkets. Supermarkets

adopt the barcode technology only if the producers of the goods move to that

technology. So this is a classic coordination problem: many

supermarkets and the producers have to move from the

old technology to the new technology of barcodes at the same

time, and because of these coordination issues

new technologies take many years to take off, and that has been the case not only with

barcode technology, but with other technologies throughout

economic history. Thank you.