God Fearing Atheist

Oh, its not that: its that SMs are conditionally disposed toward individual strategies in all situations. They dont cooperate with CMs *or* other SMs.

tronvillain

Okay, so all that's left is your interpretation of the equation p/q = {(1-u')/(u''-u')+[(1-r)u']/[r(u''-u')]}

You are only addressing the first term, and the ratio of p to q has to be greater than the sum of terms one and two. Anyway, the first term tells us that the smaller the relative difference between the "temptation" (1-u') and the "reward" (u"-u'), the more rational it is to cooperate. That's fairly intuitive.

Yes, the ratio increases - that's how the equation works. If you increase r then the p/q ratio is forced to incease, and if you increase the p/q ratio then r is forced to increase. If a population is stable at a higher r, then 1)CMs have gotten better at recognizing CMs 2)CMs have gotten better at recognizing SMs 3)CMs have gotten at recognizing both CMs and SMS or 4)SMs have gotten worse at recognizing CMs. It doesn't really look like it's becoming "more rational" to be an SM - if you increase r without any of 1-4 being the case, then it will be rational for CMs to become SMs until r is at its original value. The opposite is true as well - if you decrease r without the reverse of any of 1-4 being the case, then it will be rational for SMs to become Cms until r is at its original value.

You seemed to imply that an increase in r would result in some kind of positive feedback that would further increase r, but the mechanism by which you hoped to achieve this doesn't work. If CMs take more risks, q and p will increase proportionally, and since the ratio between the two remains constant, r remains constant. Well, that's true except in the extreme cases where q=1 and p<1 or q<1 and p=1 - the p/q ratio and r will rise in one case and fall in the other, until both q and r are equal to one.

I'm pretty sure all of that works.

[ February 01, 2002: Message edited by: tronvillain ]</p>

tronvillain

God Fearing Atheist:
Unless SMs always recognize each other, then there exists the possibility that they will both fail to recognize each other and both defect. I should think you'd want to incorporate this into your model since it decreases the utility of SMs.

[ February 01, 2002: Message edited by: tronvillain ]</p>

tronvillain

God Fearing Atheist:
I think the answer would have to be "maybe" or "sometimes." If you've got backup (which in the case of "beating the crap out of babies" is virtually everybody) the risk of reciprocation can be negligible.

God Fearing Atheist

Thats the point: they *do* both defect. They a) dont cooperate with CMs so they reap the benifits of exploitation, and b) dont cooperate with other SMs do they themselves are not exploited.

God Fearing Atheist

But how often does interaction on this larger level actually occur? I mean, many may stand side by side with the anti-baby beaters in an emotional sort of way, but few do so physically (and in any event, given the power of modern arms, i really dont think it'd be any more difficult to dispatch with a small group than it is to do with a single person).

tronvillain

God Fearing Atheist:
So defect-defect is the same as not playing? The difference between your game and the normal Prisoner's Dilemma keeps throwing me off.

tronvillain

God Fearing Atheist:
It is because we stand side by side with "anti-baby beaters" in an emotional way that we have a society where its illegal - the majority has defined it as defection deserving of retaliation.

God Fearing Atheist

[(1-u')/(u''-u')], of course, relates the gains made by defection to the gains made by cooperation. The value of defection is greater than cooperation, so the term is larger than 1. The second part, {[(1-r)u']/[r(u''-u')]} depends on r. If r=0 (that is, if there are no CMs in the population), its value is infinite. As r goes up, the value of the expression decreases to the point where r=1 (there are only CMs), and its value is 0.

One more little thing (and i'll define the numerical values up front this time :

defection = 1
exploitation = 0
cooperation = 2/3
non-cooperation = 1/3

The gain from defection, (1-u') is therefore 2/3, and the gain through cooperation (u''-u') is 1/3. Since p/q must exceed {(1-u')/(u''-u')+[(1-r)u']/[r(u''-u')]} for CM to be rational for all parties, p must be more than twice the probability of q, however great r is. So, if three out of four people are CMs, so that r=3/4, than p/q must be greater than 7/3, if r=1/2, p/q = 3...and so on. In general, p/q must be greater than 2+(1-r)/r, or (r+1)/r.



It does. As r goes up, p to q is such that is becomes more rational to adopt CM, which in turn increase r, which decreases p to q.....

[ February 01, 2002: Message edited by: God Fearing Atheist ]</p>

God Fearing Atheist

This is the PD. Defect-defect is non-cooperation...defect-cooperation is exploitation...