[PEN-L:4710] Re: collective goods problem, cont.

[Gil Skillman <gskillman@xxxxxxxxxxxx>]

In response to the following from me---

> 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.<<

----Jim writes:

>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).

Fine.  This wasn't made clear in the original post (which only spoke of
"many" players).  Radical political economy is also potentially concerned
with collective action problems in which n < 220m, so the issue of degree
vs. kind remains relevant.

Jim continues:

>But I have a question. One of the confusions (for me at least)

but not for game theorists, who are (in)famously compulsive about specifying
precisely the type of game they have in mind.

> 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?

I might return the question to Jim, since these details are not mentioned in
his original post. Furthermore, they would complicate the n=2 as well as the
n > 2 analysis, contrary to the sense of his earlier post, which posits a
qualitative distinction between the two cases (good cop/bad cop routines and
the threat of torture would affect the prospects for cooperation given any
number of prisoners).  Suffice it to say that game theorists have addressed
implications for "rational" cooperation of the sort of informational
incompleteness Jim discusses; see the Fudenberg and Tirole book mentioned
previously and below (such incomplete information problems reduce but do not
eliminate prospects for cooperation among individualistic players in a
repeated-game setting).

Second, of course it's true that real-world prisoners may not face a
repeated game,
but that's beside the point:  Jim's original question focused entirely on
comparing the 2 vs. many case when the game *is* repeated. Same point with
respect to the possibility of rule changes.

>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.

True.  All are based on the idea of punishing bad behavior as in the
tit-for-tat case.  Dilip Abreu's analysis of "optimal penal codes",
discussed in my articles with Putterman, shows the basis for these "other
strategies."

>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.

Note this is a slightly different informational problem than the one Jim
emphasizes above.  However, effective punishment strategies can still be
used even if the prisoners can't tell *who* finked, as long as they know
that *somebody* finked (see the 1992 Putterman & Skillman article, e.g.).
The punishments are in general less effective than when they can be tailored
to a particular miscreant, but the basic result is the same.

In solidarity, Gil