From: Anders Sandberg (asa@nada.kth.se)
Date: Thu Nov 28 2002 - 02:22:38 MST
On Fri, Nov 22, 2002 at 07:20:35AM -0800, Lee Corbin wrote:
> Anders writes
>
> > > > I have always thought there should be a children's
> > > > book about [tit for tat].
> > >
> > > Well, I think that *children* already understand it quite well:
> > > just observe three year olds on a playground.
> >
> > They get the tit-for-tat bit well, but they often are too
> > retaliatory. Just some fine-tuning needed :-)
>
> Too retaliatory? I guess you mean "two tats for one tit".
> But while you're at it, could you explain why EFAE (an eye
> for an eye) is not tit-for-tat? (It was claimed not to be
> tit-for-tat in some earlier post in the old thread.)
I would say TFT includes "start out by cooperation" and "only do what
the other party did last time". EFAE on playgrounds tends to be swayed
by the anger of a defection so that it turns into "two tats for a
tit".
> > One neat solution would be to have each side emplace bombs wherever
> > they want in the other side's country.
>
> I've been thinking of that! Since the U.S. can target every town
> in Iraq, wouldn't it be symmetrical and fair for Iraq to have
> smuggled in an A-bomb into every American town?
In a traditional MAD scenario it would make sense. But obviously the
problem here is the fairly clear level of irrationality of one party.
MAD is actually based on a deep level of trust in the other side to be
rational and actually care for their country (rather than personal
survival and profit). An interesting question is if MAD is possible to
sustain between two parties of different kind, such as a nation and an
individual. If superman can wipe out the US but will be covered in
kryptonite dust, is that a similarly stable situation as between two
military/political bureaucracies?
> But to return to the hard case. Let us suppose that the planners
> on both sides must accept evolution towards the table above, in
> which progressively it becomes more and more advantageous to
> strike first, and more and more dangerous not to.
>
> I submit that one can delay immediately attacking one's opponent
> by noticing that real life is not a zero sum game, and that any
> delay is a payoff. Thus, IMO, it becomes very similar to the
> finitely iterated PD.
Good point. I was setting the values as "years of progress" - a
nuclear war would be the loss of a century or so, and a year of no
war would be one year of progress.
> The finitely iterated PD goes like this. You and the other
> contestant get to play the following table 200 times:
>
> C D
> C 300,300 100,500 (denominations in
> D 500,100 0,0 Euros or dollars)
Hmm, shouldn't the values be 500,0 and 100,100?
> Now on the last round (for those who haven't seen this sort
> of thing), there is no incentive to cooperate. (The reason
> that there is some incentive to cooperate in earlier rounds
> is that it is profitable for both sides to milk the situation
> for a while.) But then when you realize that there is no
> incentive to C in the last round, there becomes no incentive
> to C in the round before that, and all the way back.
>
> So just when *would* you defect? (Of course, for newbies
> in game theory, it is not allowed to consult your altruism
> module.)
Assuming the other player was thinking as I do, I would estimate a
probability P(t) of defection when there were t moves left that was
identical to mine.
The expected value for me of the game would be
V(t) = (1-P(t))^2) (3+V(t-1)) + 2P(t)(1-P(t))(5+2t) + P(t)^2 (t+1)
Both cooperate One defects now Both defects now
So now I only have to maximize V(t) by varying P(t). Hmm, seems a bit
messy. But if P(1)=1, then it is simple to calculate V(2) and find the
P(2) that maximizes it (0.375). From that one can calculate V(3) and
P(3). A quick matlab run seems to produce a very fast decline of P(t);
only P(3) is greater than zero (0.1270). I'm sure a bit more thinking
would show why this is so.
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
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