[PEN-L:4703] collective goods problem, cont.

[JDevine@xxxxxxxxxxxxxxx]

I wrote>It's pretty well known that in a repeated two-person Prisoners'
Dilemma game, the two participants can learn how to cooperate to
avoid the dire fate of them both confessing. My reading says that
this conclusion does NOT generalize to a game with many people
(the collective goods problem) unless one abandons the assumption
that people are individualistic. Is my conclusion correct?<

Gil answers:>>Not _per se_. Rational cooperation among n > 2
"individualistic" participants can also be sustained when the
corresponding game is repeated, under a variety of conditions (which are
extensions of those which support cooperation in the n = 2 case). It *is*
reasonable to suggest that the "cooperative" solution is more difficult
to orchestrate as the number of participants grows, but this is
practically a matter of degree, not kind.<<

It doesn't matter if it's a matter of degree or one of kind, since
I was thinking in terms of N = 220,000,000 (roughly the population
of the US).

But I have a question. One of the confusions (for me at least) is
that there are two types of Prisoner's Dilemma. On the one hand,
there is the common textbook one, where each prisoner knows what
options are available to the other and what payoffs result.

On the other, we have the real-world Prisoner's Dilemma, where
neither prisoner has that kind of information (that kind of
omniscience), especially since the cops want to minimize the info
that the perps have. All a prisoner knows is "If I fink, the cop
is promising me X; if not, I'm promised Y; it's likely that the
cop is lying; and (of course) my comrade-in-crime may also fink."
The "game" is likely not going to be repeated many times (though
the prisoner doesn't know for sure) and the "rules" are likely to
change. (Also, the cops could double-team the poor perp, using the
good cop/bad cop routine to confuse him, undermining strategic
thinking. This might extend to torturing the poor guy, especially
given the current U.S. Supreme Court. ;-))

Which kind of game are you talking about, Gil?

Only the second kind of PD seems relevant. Assume, however, that
the rules don't change and the game is repeated often, in a
sequential way (and the cops can't double-team or torture). If I
understand correctly, one strategy a prisoner can follow to find a
co-operative solution (where neither finks) is to follow a "tit
for tat" ploy: if my comrade finks, I'll fink too, the next time,
to punish him; if he co-operates, I'll co-operate the next time.
Robert Axelrod has an article which shows "the emergence of
cooperation among egoists" due to that kind of strategy (where in
the first game, the perp is "nice," not finking). There are
probably other strategies that work.

But if the number of prisoners increases to 3 in this kind of
PD, the strategy tends to fall apart. Someone finks, but the
prisoner has even less information about who it was who finked. So she
doesn't know who to punish. With 4, the problem gets even worse. It
seems to me that the problem would increase exponentially with the
number of participants. In the collective goods problem, one
doesn't know at all who disconnected the smog device on his car,
polluting the air.

>what is the most up-to-date source?<

>>I don't know about the most up-to-date, but see Fudenberg and
Tirole, GAME THEORY, 1991, Ch. 5 [!], for a general treatment.<<

Thanks.

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.