[ExI] Evolution "for the Good of the Group"
avantguardian2020 at yahoo.com
Fri Sep 19 22:13:49 UTC 2008
--- On Thu, 9/18/08, Jef Allbright <jef at jefallbright.net> wrote:
> Recommended, highly relevant to much discussion here, but
> not freely available.
I am pressed for time right now so I apologize if this comes across as an incoherent screed.It seems that others are converging on the same conclusions that I have reached with my Critter's Dilemma studies. Here is a different reference regarding the evolution of altruism that some of you might be interested in.
What I have figured out is that both Critter's dilemma and PD have somewhat different "best strategies" if you are playing it against a network or group. I have been working on what I call Networked Critter's Dilemma which is very similar to what the authors of the paper in the supplied link call N-player Prisoner's Dilemma.
In essence our results tend to agree although they use computer simulations and I use graph theory, game theory, Ramsey theory, and algebra to obtain the same result. In short, while if you are playing a single round of CD or PD against an individual then you are best off defecting. But if you are playing against a group of individuals, then you might be better off cooperating, even for a single round.
I have discovered a new statistic to analyze the dilemma games in all-against-all networks. I call it the "Pareto Dividend". It is essentially the total payoff over all players in the network divided by the number of players in the network. So it can be thought of as the average payoff to every player in a network. In a *purely cooperative* network, the Pareto Dividend works out to be simply the number of players that are cooperating with you. In a mixed network, it is somewhat more complicated as you must consider all the relationships between nodes (critters) in the network. In a Critter's Dilemma Network for example, the number of relationships is (number of players)*(number of players minus one).
So lets say the temptation to defect is 2 points of utility. If you are playing in a network of 3 players, all cooperating, then your pareto dividend is likewise 2. In other words cooperating with 2 other players is as profitable as defecting against any single player and carries no risk of retaliation.
The problem in however is that a player in a Critter's Dilemma network can ignore while his peers all cooperate and thus get a free ride, getting an only slightly diminished Pareto Dividend for doing nothing. Of course if enough players ignore, then the Pareto Dividend drops below the level of the temptation to defect. And once players start defecting on one another, the Pareto Dividend becomes negative.
The good news is that the Ramsey Theorem makes it nearly impossible in sufficiently large networks that at least a few individuals don't cooperate, even if it is entirely by accident. In other words small groups of the stupidest pieces of protoplasm will inadvertantly cooperate by sheer random chance if there is a enough of them and as soon as they do, they will aquire a selective advantage over their non-cooperative neighbors as long as they can somehow recognize their own.
I will write a more cogent explanation later but in the meantime try answering the following questions which my new theory of networked games can answer quite readily:
How many possible ecosystems are there for a dozen species? How many possible economies are there with a dozen participants? The answer is the same for both and it is an exact number.
"See them clamber, these nimble apes! They clamber over one another, and thus scuffle into the mud and the abyss."- Friedrich Nietzsche
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