in this sub-unit we're going to look

at the prisoner's dilemma which is
perhaps

the earliest idea model for

studying cooperation in social science
and

political science among other fields.
The prisoner's dilemma

is based on a metaphorical story.
So here's the story

Alice and Bob have collaborated on
committing a crime

and they can caught and thrown in jail

they're not allowed to talk to each
other there's no possible way that they

can communicate

and the police are offering a deal

that involves one testifying against the
other. Police don't have quite enough

evidence to convict them on the charge
they want to convict them on

so they're going to try to get 1 of
them to testify against the other one

Here's the deal: if neither them

testify the police are going to have to
reduce the charge

and each one will get five years in
prison

However if Alice decides to keep silent

but Bob decide to testify against her
Alice is going to get life in prison

and Bob is gonna go free.The same
applies to Bob

if he keeps silent but Alice testifies
he gets life in prison

and Alice goes free.Now they both
testify against each other

there each gonna get 10 years in prison

They both offer this exact same deal
with no communication they have to

decide what to do

So should they stay silent 
or justify.

what would you do if you are Alex.Here's
how Alic's thought process might go.

Suppose Bob keeps silent

if she keeps silent so she gets five years
in prison

and if she testifies she gets off

scot-free, so in that case you should

clearly testify.Now suppose Bob
testifies

well in that case Alice keeps silent she
gets life in prison

have she testify she gets 10 years in
prison which is better than life in

prison.

so she should testify in that case as
well. The only problem is

that bob is going through the same
thought process

and concludes that in each case he
should testify

so what happens is they both decide to
testify

and they both get ten years in prison

where's they would have only got five
years in prison if they had only

cooperated with each other and kept
silent.

Question is what could have convinced
them to stay silent?

prisoner's dilemma was originally
invented by

to mathematical game theorists Flood 
and Dresher

in the 1950s at the high of the cold
war between the United States and the

Soviet Union

it's been used as a metaphor for real
world cooperation issues

in arms races, wars,
global warming

and many other phenomena. It's also one
of the most

famous and influential idea models in
social science

If your're social scientist I'm guessing
you probably heard of it

we can gauge a little bit if it's fame
and influence by

looking on the Google Scholar page and

the prisoner's dilemma gets thirty four
thousand results. Versions of it

discussed by Garret Hardin has been
famously called the tragedy

of the common. the tragedy is that it's
always in

an individual's best interest to not
cooperate

but if everyone does not cooperate

than everyone gets a worse result in the
words of political scientist

Robert Axelrod the pursuit of
self-interest

by each leads to a poor outcome for all
Robert Axelrod

is a political science professor at the
University of Michigan

who is been studying the prisoner's
dilemma

and variants of it for over 30 years.

he written two very influential books
on this topic

one called the Evolution of cooperation
and the second called the Complexity of

cooperation.

cling to Axelrod his main motivation

for learning about effective strategies
was to find out help cooperation could

be promoted

in international politics especially
between the East and the West during the

Cold War.

and its main question is under what
conditions

will cooperation emerge in a world of
egoist

without central authority. This remains

of course an extremely important
question today.

when scientists study the prisoner's
dilemma

they typically phrase it in terms of
that game with two players

so are two players are Bob and Alice, and
Bob and Alice

decide to either cooperate which would
correspond in

your story to staying quiet so they're
cooperating with each other

or defecting that would correspond to
testify against the other one

they receive what's called a payoff

the payoff is given by is payoff matrix

now here we're going to depart from our
prisoner story and we're going to assume

that

the higher the pay of the better in this
payoff matrix

if Alice and Bob both cooperate

Alice here in red gets 3 points
and Bob get 3 points

it Alice cooperates and Bob defects

Alice gets 0 and Bob gets 5. 
If Alice defects

by cooperates the opposite happens Alice
gets 5 and Bob gets 0

and they each get 1 point if they both
defect

so these numbers aren't the same as in
our prisoners story but the idea

is the same

Alice can reason that if Bob cooperates

the best thing for her to do is to
defect and if Bob defects the best thing

for her to do this defect

so in both cases Alice will decide to
defect

again the goal is to get as many points
as possible regardless of what the other

player gets

so this is not a competitive game, it's
about individuals trying to maximize

their own pay off

on one round each player either
cooperates artifacts and there's no

prior communication

between the two players. Axelrod's
question was this:

suppose that the game is iterated

that is the players play for several
rounds

remembering perhaps what the other
player did on previous rounds

how is it possible that reciprocal
cooperation

can be induced to study this question

Axelrod devised two tournaments

in which he invited well-known political
scientists

other social scientists, mathematicians,
game theorists

to submit strategies to play against one
another

strategies played iterated games against
one another in

a round-robin fashion that is each
individual played against

every other individual and played
several games against every other

individual

some people submitted very complicated
strategies that created

complex statistical model serve other
opponents

and did quite a bit of computation. These
strategies were all

given as computer programs and it turned
out that

the winner have both the tournament's
was the simplest evolve strategies known

as tit-for-tat,

which is submitted by Anatole Rapoport
mathematician

what tit-for-tat does it start up by
cooperating

and then it each successive round it
just does with the other player did on

the previous round

so if the other player cooperated on the
previous round

to tit-for-tat cooperates, if the other
player defected in the previous round

tit for tat defects

so it for warts cooperation with
cooperation and

punishes defection with defection
incredibly simple

but it was the winner. the NetLogo
models library has a number of

prisoner's dilemma models we're gonna
look at two of them

but before we do that I'm gonna have you
take a quiz to make sure you understand

what we've done so far in this subject