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