From: throopw@sheol.UUCP (Wayne Throop)
Newsgroups: rec.arts.sf.written,rec.arts.sf.science
Subject: Re: Moties and the prisoner's dilemma
Summary: "iterated" doesn't really imply "pseudo"
Date: 04 Sep 92 21:57:41 GMT

> From: morlan@afit.af.mil (Bruce W. Morlan)
> Message-ID: <1992Sep1.122427.7749@afit.af.mil>
>> throopw@sheol.UUCP (Wayne Throop)
>> I didn't see the notions of the iterated prisoner's dilemma's impact on
>> evolutionary thought applied to the question of the Moties [...]
> The formulation of the prisoner's dilemma is tricky.  IMHO, any payoff
> matrix that allows infection and eventual overcome of a pure defect
> strategy population by a TIT-FOR-TAT group probably is not a "true"
> prisoner's dilemma situation.  

Depends on what you call a "true" prisoner's dilemma.  Note that
I was careful to call it an "iterated prisoner's dilemma".  The situation
discussed by Dawkins where invasion of the stable "always defect"
population by TFT players is actually a local, multi-threaded, iterated
prisoner's dilemma.  The important features are:

       iterated:        players may use the history of plays to decide,
                        and (also important) do not know if the current
                        play will be the last one (hence, will be used
                        in future play)
       multi-threaded:  players remember who they played against
                        in past rounds when considering history
       local:           players occupy a space, and tend to play rounds
                        against other players close to them in the metric
                        of this space, and not against  players far away

Without the "iterated", it's better to defect.  Without the
"multi-threaded", you don't have information to play TFT.  Without the
"local", it is prohibitively difficult for TFT to invade a consolidated
"always defect" population. 

The actual payoff matrix used in each round of play is a true prisoner's
dilemma matrix.  But the total situation isn't a single round of play. 
The goal is to maximize your own (NOT the population's) total payoff
from many rounds of play.  (The goal in simple PD is to maximize
your payoff from a single round of play.  It is frustrating to many
philosophers that logic dictates "always defect".)

So, yes, the total situation isn't a true PD, but I'd hesitate to call
it "pseudo" either.  I'd recommend reading the account in Dawkins' "The
Selfish Gene", or (I think) the same stuff covered in essays in
Hofstadter's "Metamagical Themas" book.  (Though note that Hofstadter's
additional conclusions about single-shot PD in homogeneous populations
are somewhat controversial.)

> A prisoner's dilemma
> situation should be unstable for cooperation.  I believe that one
> of the referenced works gives the exact range of payoff ratios that
> result in a prisoner's dilemma.

Unstable for cooperation *in*any*given*round*in*isolation*, yes. 
Dawkins also gives the criteria for the per-round payoff being a true
PD.  He uses this one as an example:

                                         opponent plays:
                             cooperate                          defect

           cooperate       reward: 3 points      suckers payoff: 0 points
 if I play:      I get:
           defect      temptation: 5 points          punishment: 1 point

There are various technical reasons why the temptation must be greater
than the sum of the reward and the punishment, hence (I think) if
the temptation were 4 points, it would't be a true PD.
--
Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw
Newsgroups: rec.arts.sf.written