> A historian, following current norms of historians, should not
> say that vN and M had an equilibrium concept for cooperative
> games. They had an equilibrium concept for GAMES, full stop.


Well, which concept is that?  The minimax solution, or the
one for what we now know as cooperative games?

> Consider a 2P0S game in which binding contracts are allowed. I
> don't see how the solution would be other than the minimax
> solution. That is, the distinction between cooperative and
> non-cooperative games seems to me moot for 2P0S games.


Notice "the minimax solution" is a solution for non-cooperative
games.  Obviously, zero-sum games are uninteresting if
cooperation is allowed, but vNM were considering what we
now call the non-cooperative case.

>>> One can easily find the minimax solution to a 2P non-constant
>>> sum game by setting up two Linear Programs, one for each
>>> player. The solutions will give a (mixed) strategy for each
>>> player.


>> Great, I didn't know that.  Now show how (defect, defect) 
>> isn't the unique non-cooperative equilibrium for the 
>> single-shot PD using this notion of equilibrium.

> Why would I want to do that? Such a nonsense claim would not
> defend anything I've written.


I suggested (D,D) was the only sensible equilibrium for the
PD, regardless of which concept of "equilibrium" one uses.  I
included vNM's solution concept for what we now know of
non-cooperative games in a brief list of such concepts.  Robert
balked at the idea.  But it would now seem that Robert agrees
that (D,D) is the unique equilibrium for the PD.

It should not need to be said because it is implied, but just
to avoid confusion: Yes, I mean the PD when it is played without
binding contracts.  The different game in which binding 
contracts are allowed is not a "dilemma," is not interesting,
and is not what everyone but Robert thinks of as "the" 
prisoners' dilemma.

> Notice where poor Chris Auld places the adjective "non-cooperative"
> above. It's as if he momentarily recognizes that one can talk
> about the cooperative equilibrium for a PD payoff matrix.


Who wrote this?

   Anyways, I suppose it's worth pointing out that      
   treating the PD as a cooperative game, while not "wrong" in
   any formal sense, entirely misses the point.

The key point, of course, is that if one assumes, as Robert
did, that "the players can agree on probabilities beforehand,"
one is now talking about a different game than that which
everyone refers to as "the prisoners' dilemma."

>>> Consider the PD as an uninterpreted payoff matrix. One can
>>> go through the mathematical calculations to determine the
>>> vN and M solution. And one can equally well calculate the
>>> Nash equilibrium. These solutions are different.


>> For the n-th time: Bob, if you assume that players can
>> contract over outcomes, then you talking about a 
>> DIFFERENT GAME. (C, C) is *not* "the vNM solution" to
>> the *non-cooperative* PD...

> I don't know why poor Chris Auld keeps on repeating irrelevancies.
> I neither say that (C, C) is the vNM solution nor that the
> vNM solution solves the non-cooperative PD. Why does he
> think the word "uninterpreted" appears in the above paragraph?


Why does Robert think that ignoring the rules of the game helps
him make this odd case?  If he wants to be picky, I will amend
my remark above to "the set of points that constitute the vNM
solution, which includes (C,C)."  That doesn't change my point.
"The" vNM solution applies to the game where players can contract
over outcomes.  If such is not part of the available strategies,
it's simply irrelevant.

> A distinction known now, but not when the PD was invented,
> cannot necessarily be used in a historically acccurate
> construction of what Flood and Dresher were up to.


But is should be used in an historically accurate description
of "what Flood and Dresher were up to."  If Flood's insight
was that if people sit down and repeatedly play this game
against each other they won't always play (D,D), then that
was clever.  We should say he "invented the iterated PD to
investigate if people would play Nash."  That he didn't
call it the "iterated PD" is semantics.


>>>>>> Anyways, I suppose it's worth pointing out that 
>>>>>> treating the PD as a cooperative game, while not "wrong" in 
>>>>>> any formal sense, entirely misses the point. The reason that

> I should hope he would in telling his history. There is no such
> thing as "THE point" independent of all context.


There are of course fifty years worth of literature which brings
up points related to the PD.  Again, assuming away individual
incentives to defect "misses the point" of the prisoners'
dilemma.  "Misses the point" is a rather common turn of phrase
most native English speakers, or folks who scored in the lowest
decile on TOEFL for that matter, understand.

> But above he seems to have lost track of the fact that the
> players are better off under (C, C), and for all other but two
> points in the vN and M equilibrium, than they are under (D, D).
> The vN and M equilibrium is, in some sense, better than the
> Nash equilibrium.


If Robert merely meant that the players would "be better off"
under (C,C) than (D,D), he is stating the blindingly obvious.
In context, his line of argument implied he meant that play
in the experiment reveals (C,C) is "better" in the sense it
is empirically validated, which is mistaken.  So, Robert was
either stating the obvious for no purpose, or he was 
misinterpreting the empirical evidence.


>> It is not silly to point out the perfectly obvious fact
>> that the reason the PD is so important in so many fields
>> is precisely that the robust equilibrium is individually
>> optimal but socially suboptimal.  It is not silly to
>> point out that allowing the players to write binding
>> contracts to get to the optimum simply assumes the issue
>> away and renders the PD uninteresting.  No one -- no one --
>> with any familiarity with these issues would disagree
>> with that.  Indeed, anyone insisting that that point is 
>> "silly" clearly doesn't have any idea what he's talking 
>> about.

> Anybody that has read what I have written with understanding
> would see that poor Chris Auld's paragraph is a complete
> non sequitur.


Robert, immediately after presenting his pointless cooperative
solution to the PD, referred to the ideas presented in the 
paragraph above as "silly." 


>> [ Stupidity deleted ]


I have removed all of Robert's other insults, except I have
left "poor Chris Auld" in all it's many repetitions.  I wish
Robert could get a single post out without being relentlessly
"argumentative and ill-tempered," although I suppose I must
admit that his arguments become more and more compelling the
more times he insults me.  Perhaps someone will offer him
a faculty position in an economics department if he writes
a "long essay" titled "Chris Auld is a doodyhead."  Worth 
considering anyways.

I suppose it's worth  pointing out, again, that no one with 
even a modest understanding of game theory would disagree 
with any of the points I've made in this thread.  This is
hardly advanced stuff.

I would also note that we started off with a broad 
discussion, yet in his last two posts Robert plainly insists 
the only point of discussion is Flood's intent circa 1950.  
Robert is not even correct on that trivial point because he 
insists a rose by any other name is a tractor, but it would 
seem to be the only point he thinks he has a chance of 
winning.