WEBVTT

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>> Let's talk a little
bit about game theory.

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Some times in economics
people want to be able

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to describe situations

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that involve what we call
strategic interaction.

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Strategic interaction just means

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that now not only does your pay
off, your profit, your utility,

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how ever you want to think about
it depend on your own choices

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but it also depends on the
choices of other people

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in your market, in your
industry and so on and so forth.

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Typical examples of strategic
interaction usually involves

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decision among firms
regarding whether

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to cooperate or to compete.

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We're going to go
over and example

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that has a slightly
different context known

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as the prisoner's dilemma where
people are deciding whether

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or not to confess to
a particular crime.

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The set up of the prisoner's
dilemma is a tad bit contrived

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but it goes as follows.

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Imagine a situation in
which two people are brought

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in for supposedly
committing a crime.

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Now these two people are
held in separate cells

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so they can't talk to
each other and even

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if they could they couldn't
somehow contract on whether

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or not they were going
to confess to the crime.

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The people are then
brought in individually

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and asked do you confess
or do you not confess?

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We can represent the pay off's
to that sort of situation

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in a table as follows.

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You'll notice here that we
have player 1 and player 2.

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I made things nicely color coded

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such that we have player 1's
pay off's in terms of utility

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in blue to match play 1 and
player 2's pay off's in terms

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of utility in green here.

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So you'll notice that if neither
player confesses they just sit

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there and hold tight, they
each get a pay off of 10.

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If the first guy keeps quiet
and the second guy rats him

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out the second guy gets 15 while
the first player gets nothing.

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The opposite happens here
if the first player rats

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out the second one, now
the first player gets 15

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and the second player
gets nothing.

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And if they both try to rat
each other out, they both end

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up with 5 meaning they're better
off than if they just sat here

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and had the other guy
rat him out but not quite

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as well off collectively
as if they both kept quiet.

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The question then becomes given
this structure what's going

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to happen.

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In reality both players are
making the decision of whether

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or not to confess at the same
time but let's just pretend

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that they can guess or somehow
know what the other person is

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going to do and we can ask a
number of hypothetical questions

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as to what the best response
is for these players would be.

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So let's take the
first case here,

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say if player 1 confesses
what should player 2 do?

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In other words what's
player 2's best response?

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Well, we can go over here,

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we say if player 1
confesses we're somewhere

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in the bottom here and player 2
can either get zero by holding

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out and being quiet or he
can get 5 by confessing also.

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Five is strictly better than
zero so if player 1 confesses,

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player 2 also wants to confess.

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Now what about if
player 1 doesn't confess,

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well if player 1 doesn't
confess we're up here

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so player 2 again has two
options, he can get 10

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by keeping quiet or he can get
15 by ratting out his buddy.

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So 15 is better than 10 so
if player 1 doesn't confess,

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player 2 still should confess.

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Notice here that's interesting
that player 2 his best option is

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to confess regardless
of what player one does

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or alternatively put
player 2's best option is

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to confess regardless of what he
thinks player 1 is going to do.

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This type of situation is
called a dominant strategy

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in that confess is
a dominant strategy

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for player 2 meaning it's
always the best regardless

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of what the other guy does.

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Think about this the other way
around, say we make some guesses

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as to what player 2 is going
to do and then when we say

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in each case what's player 1's
best response in that situation.

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So if player 2 confesses,

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what's the best thing
for player 1 to do?

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Say if player 2 confesses
we're over here

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on the right somewhere we
say player 1 can either get 5

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by confessing or 0 for being
quiet this problem is looking

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strangely familiar, say
well 5 is better than 0

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so player 1 is going
to want to confess.

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Now if player 2 doesn't
confess what should player 1 do?

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So if player 2 doesn't
confess, we're over here

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on the left somewhere and
player 1 can either get 10

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by being quiet or 15 by
ratting out his buddy,

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well 15 is greater than 10 so
he's going to want to confess.

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Notice here that
because we confessed

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in both cases confessing
is also a dominant strategy

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for player 1.

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So here I've circled player
2's best responses in green

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and I've circled player
1's best responses in blue

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and you'll notice there's one
place here where they over lap

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to say that in this situation
where both parties confess both

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of them are responding
as best they can

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to what they think the other
person is going to be doing.

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We say that this situation
here is what's called a Nash

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equilibrium; more formally put a
Nash equilibrium is a situation

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where each player's
action is the best response

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to the other player's actions.

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In a situation where the players
are all moving simultaneously

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this basically means that
each player is reacting best

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to what they think the
other person is going to do

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and they're actually
right in their guess

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of what the other
person is going to do.

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[ Pause ]

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Notice here that the equilibrium
outcome actually...it doesn't

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look as good as it could
because here we're saying

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that any equilibrium when
people are acting according

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to their own best interest each
of them ends up with a payout

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of 5 where as if they only
cooperated they would each get a

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payout of 10.

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We can say here that there can
be a perato improvement going

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from both parties confessing
to both parties staying quiet

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in that both parties
would be made better off

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and nobody would
be made worse off.

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Unfortunately, due to
the competitive nature

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of the this game that's
not what's going to result

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because it's really hard when
there's no contracting involved

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to guarantee regardless of
what the other party says then

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when it comes down to it
they're actually going

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to cooperate given that it's

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in their interest
individually to not cooperate.

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So one question that
economists like to think

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about is then how can
cooperation be sustained

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in the real world?

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Well, one thing that's
important to remember here is

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that in the real world this
game isn't played just once,

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when you have firms interacting

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with each other people making
these decisions often times they

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have the chance to make the
decisions over and over and over

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so when you have what's called
a repeated game you might have a

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situation where people
start testing out the waters

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to say well maybe if I
cooperate the other guy's going

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to cooperate and then
we can keep this going

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because to cooperate here and
hope for the best outweighs,

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you know there's this
threat of well if you try

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to screw me one time we're
reverting back here actually

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gives in the long term an
incentive to cooperate.

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So like I said it seems a little
bit artificial to be talking

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about this context of
prisoners being interrogated

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because really we're
talking about economics.

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But it's very easy to see how
this situation could be relevant

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in an economic context by just
replacing the intuition behind

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some of the choices.

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So what I did here is
set up the identical game

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and have this model as
still player 1 and player 2

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but now they have the
choice of whether or not

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to cooperate or to compete.

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And you can see here they'd both
do better off by cooperating

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but they also all have the
private incentive to compete.

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And you can notice here

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that this situation is
actually pretty realistic

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because at least in the United
States firms are not allowed

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to contract on whether or not
they're going to cooperate,

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that's called collusion,
it's illegal.

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So they really are
simultaneously making

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independent choices as
to how much to cooperate

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with their ''competitors''.