[PEN-L:4719] collective goods problem once again

[JDevine@xxxxxxxxxxxxxxx]

Sandy writes: >>One application where the iterated prisoner's
dilemma does provide some useful insight, I think, has to do with
price and non-price strategies among oligopolists, where one can
theoretically support cooperative behavior regarding the former,
but not the latter.... <<

Let's start again. I was not (and am not) criticizing game theory
(though I might criticize those who apply game theory
inappropriately but no-one here is doing so). I think game theory
is quite appropriate to small-group problems like oligopolistic
rivalry or "team production" (as long as we don't stop with game
theory and see it as the _whole_ story).

Restate the question: in a small-number Prisoner's dilemma (PD),
as with oligopoly, over time the "players" can learn to cooperate
(tacit collusion) -- even when there is incomplete information
about who is defecting or finking.  Or at least that is how I
understand the literature.

But suppose we have a large-number PD (the collective goods
problem). There are some-odd million people in Greater Los
Angeles (and some of them are quite odd). The problem is
pollution and whether or not to disconnect the smog device on
one's car (which lowers gas mileage and of course raises the
price of the car). The simple individualistic incentive (assume)
is for me to disconnect the damn thing. I can get the benefit of
everyone else keeping their devices connected (i.e., cleaner air)
and good gas mileage too. If I disconnect ("defect"), no-one will
know, since the device is inside the car. Of course, if everyone
is individualistic like me (looking out only for number one), we
all "defect" (free-ride) in this way and the air ends up being
polluted. The optimum (assume) is for us all to cooperate, to
keep the smog devices attached, with the benefits of clean air
more than paying for the costs of low gas mileage.

Now, if the 2-person game result (of prisoners learning to
cooperate) applies at the many-person level, we will
spontaneously (in a decentralized way) figure out a way to make
sure that there are no (or few) defectors or free-riders. Of
course, this spontaneous learning process will be slowed if the
rules change in the middle of the game, etc.

On the other hand, if the two-person game result does NOT apply,
then in order to solve the problem of smog we have to either

(1) change the structure of the game by getting together
politically (outside of the given structure of the game) to
create an anti-smog agency which _forces_ us to put our cars
through smog tests (and makes sure that the smog check guys are
honest, too). (Alternatively, the gov't could push us to use
public transport.) If the government agency is successful, the
application of fines changes the costs and benefits in the game
matrix, so that it is no longer a PD.

or (2) change the structure of the game by positing that people
get some jollies (a.k.a. utility) from being honest and/or from
making some contribution to society's betterment. This changes
the "game matrix" because the benefits of "defecting" are reduced
(and those of cooperating increased) by the introduction of these
"higher" motives. This again makes the "game" no longer a PD.

Of course, L.A. has an extremely individualistic culture, so the
latter seems unlikely. In fact, the former has been applied
(though the commitment to public transport has been a bust,
meaning investment of billions in a boondoggle subway system at
the expense of busses).

The qualitative difference between the few-person PD and the
many-person PD (collective goods problem) is that the latter is
not simply an adding up of "dyadic" (2-person) games [at least
according to the articles by Braybrooke and Hardin in Campbell &
Sowden, eds., PARADOXES OF RATIONALITY AND COOPERATION:
PRISONER'S DILEMMA AND NEWCOMB'S PROBLEM, University of British
Columbia Press, 1985]. The many-person game is one of a
relationship between each individual and the somewhat ephemeral
"public as a whole." According to these authors, at least, to see
the collective goods problem as a large number of dyadic games is
to fall for the fallacy of composition.

Please correct me if I'm wrong.

in pen-l solidarity,

Jim Devine   jdevine@xxxxxxxxxxxxxxx
Econ. Dept., Loyola Marymount Univ., 7900 Loyola Blvd.
Los Angeles, CA 90045-8410 USA
310/338-2948 (daytime, during workweek); FAX: 310/338-1950
"It takes a busload of faith to get by." -- Lou Reed.