Hi. In this lecture, we're gonna extend
the core idea of the prisoner's dilemma,
where it's in my individual benefit. To
[inaudible], to defect. But collectively,
we're better off if we cooperate. What I
mean by extend is this. In the prisoner's
dilemma, it's a two player game. But more
generally, we can think of N person
prisoner's dilemma, where, when I
cooperate, lots of people benefit, not
just one. And what we wanna see is how
those differ from the standard prisoner's
dilemma, and see how those also sort of
apply in some real world cases. So the
first thing we're gonna talk about is what
is called a collective problem. In a
collective action problem, I make some
choice. Do I contribute? Now, there's a
cost for me to contribute. But there's a
benefit to everyone else. So, how do we
write this? We write this as follows. We
say, let's let X J be the action. >> Of
person j. And what we'll assume is that XJ
is some amount of effort. It could be
anywhere between zero and one. It's how
much you are contributing to the public
good. Now there's a cost. So the more I
contribute XJ, the more it costs me. So my
payoff is negative in my action. So
therefore you think I should choose XJ to
be zero, and that's, sometimes like
defecting in the prisoner's dilemma.
However we also assume, that there's a
benefit, Which is the sum. This, this sign
here means the sum. It's the sum, of all
of the Xi so of all the people in society,
so collective we'd be better off if
everybody put it on big XI and XI be one
but individually we don't want to. >> Now
what we assume here is we see this term
beta is between zero and one. If beta were
bigger than one, that would mean to be
that my interest to cooperate. Because it
would it, my cost would be minus XJ, but
then I'd be getting beta times XJ, and
beta's bigger than one, so I'd be better
off. So we see that beta's in zero one. So
my collective benefit from doing this
thing is actually less than my individual
cost. Let's look at an example. Let's
suppose that there's ten people, and we're
going to assume that beta is equal to.6.
Now let's with everybody else is
cooperating. So, let's suppose I'm X one,
and that X two equals X three equals X
ten, equals one. So, everybody else is
doing one. So my payoff if I choose X one
equals zero is just gonna equal zero
plus.6 times nine, which is 5.4 If
everybody else is cooperating. So there's
nine people cooperating so I'm gonna get.6
times that which is 5.4. Which is great,
If I were to cooperate. It's gonna cost me
one, and what I'm gonna get though, is I'm
gonna get. Point six times ten which is
six minus one which is five, 5.4 is bigger
than five so it's in my interest to put XY
equals zero. But collectively everybody
else would be better off if I would choose
XY equal to one. So again this a lot like
the [inaudible] dilemma but instead of me
playing against one person I am playing
against a whole bunch of other people.
Where does this apply, well think of
things like carbon emissions. It's in our
collective interest if we reduce carbon
emissions, so if I sort of, you know, put
forth effort to, you know, put less carbon
in the air. But it's costly for me to do
that. And so, what happens is over time,
we've had lots more carbon emissions,
probably more than we'd ideally like to
have, because it's a collective action
problem. Now, sometimes these are called
free rider problems. And they're called
free rider, because it's in their interest
to free ride off the good will of everyone
else. I'd like everyone else to cooperate,
but I don't want to. Now, there's another
type Of sort of N-person prisoner's
dilemma, which is called a common pool
resource problem. And this differs a
little bit from the collective action
problem. Let me explain how. In a common
pool resource problem, we've got
something. Let's say, like, cod in the
ocean. And if we fish those too much the
population gets smaller and the population
can't reproduce itself. So what we're
trying to do is manage some resource that
has the possibility of reproducing itself.
Let's see how this would work. Let's
suppose now that I've got to decide how
much cod to eat, And so we'll let XJ equal
the amount of cod that I eat, how much I
fish out. And we'll let X be the total
consumed. That's the sum of what everybody
does. And what we'll assume that the
amount of cod available next period is
just the cod that was available this
period minus what was eaten squared. So
we'll assume the can mate and, you know,
reproduce and make more cod. And so the
more we eat, the fewer there are to
reproduce. So, let's do an example. Let's
suppose that the cod population is 25, and
let's suppose that we eat twenty. So if we
eat twenty, and how much gonna be
available next print, well just 25 minus
twenty squared which is 25 so we've got a
nice stable equilibrium here. We're gonna
have 25 cod this period, 25 cod next
period, 25 cod the period after that,
everything's gonna be perfectly great. But
what if I say, you know, I'm gonna have a
party, let's have a big cod fest, and lets
you know, I'm just gonna consume more cod
than I'm supposed to. And that's gonna
drive. X one up to 21. So now collectively
we're getting 21 units of cod. Well how
much are we going to have next time? Well
next time we're going to have 25 minus 21
squared, which is four squared, which is
sixteen. Well if we've got sixteen, and
we've got a problem because in the past
we've been eating twenty units of cod.
20's bigger than sixteen. We're going to
run out. And the cod's all going to go
away. And you might think, okay, that's,
doesn't make any sense, but if we think
about it, there's lots of cases of that
happening. There's a famous book written
by Jared Diamond called Collapse where he
talks exactly about this problem. That
you've got a society of people whether
it's the people in Finland, whether it's
the people in, you know, [inaudible], or
these people on Easter Island. And what
you get. Is over fishing, over consumption
and eventually the resource goes away. So
in the case of Easter Island what you see
is the population was getting bigger,
bigger and bigger , and then there was a
collapse and the collapse happened when
the forests were completely destroyed. >>
They kept, sort of harvesting too much
wood, and the forests couldn't reproduce
themselves, and what happened is, they had
a collapse of the society. If you look at
present day Philippines, this is a graph
showing the total forest covering and you
see that it was very high, and then
suddenly, it's fallen away really quickly,
again, over harvesting the forest. Now the
Philippines likely a part of the global
economy, they can trade for things that
they used to get from the forest, but if
they were isolated like the people on
Easter Island, they too would have
collapsed. Previous lecture we talked
about, look we've got all these ways to
overcome these things. Repeated games,
reputation, networks, group selection, kin
selection, incentives, prohibitions, all
sorts of stuff that we can do in order to
get cooperation. Well those prefer sort of
two person problems in most cases, and
they ignore a lot of the particulars. So
we think about con, that's a very
different thing than thinking about
forest, and this is gonna be a very
different thing than say, cattle grazing
on the commons. So when we think about
these collective action problems or these
common police horse problems we realize
that each one in and of itself is
particular. So the way we're gonna have to
solve it, we're gonna have to do
cooperation is gonna depend on the
circumstances of the problem itself. The
particulars are gonna matter. And that's
where we're gonna go in the next lecture.
We're gonna talk about how you solve
collective action problems and chemical
resource problems in the real world. All
right. Thank you.
