4.2, equilibrium in the invisible hand game.
In this section I would like to talk to you about a very easy method that you
can use to find equilibrium in simultaneous game, and
that method is called the best response method. Now let's
scroll down.
This is the invisible hand game. We got two players, Anil and Bala.
They have to make a decision between growing either cassava or
rice. They have to make this decision at the same time,
and they cannot talk to each other while making this decision - they cannot
coordinate with each other. Now are there any Nash equilibria in
this game? For that we need to put ourselves in the
shoes of the players and analyze the game from their perspective.
I'm now going inside Anil's head and look at the game.
A'm Anil and now. What am I going to do if Bala decides to produce rice? What is
my best response if Bala decides to produce
rice? If I produce cassava I'll get four, for rice
I'll get one. So my best response in this situation is
to produce cassava. Remember: this is not actually happening,
this is just a thought process in my mind - in Anil's mind. So to
remember my best response under this
possible scenario I'll put a full dot next to cassava. The dot
represents my best response - Anil's best response.
Now what am I going to do if Bala decides to produce cassava?
If I produce cassava I'll get 3, for rice I'll get 2. So again I decide to go
for cassava. This is my best response if Bala decides to produce cassava. So
again I'll put a full dot
next to cassava to mark my best response strategy.
Now I get out of Anil's head and go inside Bala's head
and do the exact same thing. I'm bala now. What's my best response if Anil produces rice?
If I produce cassava I'll get two,
for rice I'll get three, so in this case I'll produce rice, and just to remember
my decision, to remember my best response, I put a
circle in this cell, which corresponds to my decision - Bala's
decision to produce rice if Anil decides to produce rice.
Now what if Anil decides to produce cassava?
If I produce cassava I'll get one, for rice I'll get four,
so again I decide to produce rice and for that
I put a circle around this cell to mark my best response
strategy of going for rice now. Let's get out of Bala's head
and look at the game from the perspective of an
outsider. We realize that both players have a dominant strategy:
Bala is going to produce rice no matter what Anil does,
Anil is going to produce cassava no matter what Bala does.
We also realize that we have one Nash equilibrium in this game,
and this cell represents that equilibrium where the best response
strategy of both players coincide. Remember: the full dot represents the
best response of Anil and the circle represents the
best response of Bala and in this cell both best responses
meet each other. So what's the Nash equilibrium in this game?
Four and four? No, that's a typical answer which is wrong. Remember: Nash equilibrium
is a decision, not a number, and in this case the equilibrium is Bala
producing rice and Anil producing cassava.
Now in the end, let me just leave you with a question to think about:
why do you think we call this game the invisible hand game?
Thank you.