The Parasite Dilemma

[thylacine]

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The Traveler's Dilemma has inspired me to create this Parasite Dilemma. I wonder if it's an innovation or if someone else has already invented it. If it's an innovation you saw it first here on SMP.

The Parasite Dilemma
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You are part of a group of 100 people. Each person in the group writes down on a piece of paper their decision whether to be a Contributor to the Group or a Parasite on the Group. The Operator of the experiment will add $100 to the Group's Treasury for every Group Contributor. For every Parasite on the Group, $200 will be subtracted from the Group Treasury, which may go into debt. Each Contibutor gets 1 Share and each Parasite gets 2 Shares in the Treasury. The Treasury is then divided amongst the Contributors and Parasites according to their Shares in the Treasury. If the Treasury is positive each Parasite will recieve twice as much of the proceeds as each Contributor. On the other hand, if the Treasury is in Debt each Parasite must pay out twice as much as each Contributor to pay off the Debt.

What is your decision? Do you decide to Contribute to the Group or be a Parasite?

There is also a NonDebt version of the Dilemma where the Treasury cannot fall below zero. What is you decision in the NonDebt Version?

PairTheBoard

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Getting back to the original problem as formulated, this is a multiplayer game with at least one Nash equilibrium. My guess is that there is just one such equilibrium, namely each player chooses Contributor with exactly the same probability about p=0.6833, and chooses Parasite with probability about q=1-p=0.3167

That way the expected Treasury is about $500, giving a break even choice between getting 1 share of 500+100 or 2 shares of 500-200. Some approximations have been made, so the exact correct value of p would be slightly different.

OK?

NonDebt version: p would be somewhat less such that again the expected Treasury is about $500.

[CallMeIshmael]

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If I feel everyone is going to contribute, why wouldnt I play parasite?


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Because of a reason you haven't thought of. A reason that depends on creative thinking. A reason that takes you outside your box of logic. A reason that the professional theoreticians are still working on formulating. A reason you will never discover unless you look for it.

PairTheBoard

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Can you enlighten us?

Or, is your answer, "you're wrong, but I just dont know why you're wrong"?

[PairTheBoard]

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If I feel everyone is going to contribute, why wouldnt I play parasite?


[/ QUOTE ]

Because of a reason you haven't thought of. A reason that depends on creative thinking. A reason that takes you outside your box of logic. A reason that the professional theoreticians are still working on formulating. A reason you will never discover unless you look for it.

PairTheBoard

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It seems to me that you are complaining that game-theoretical analysis of a 1-time Prisoner's Dilemma doesn't apply to iterated Prisoners' Dilemmas. Pure parasite strategies tend to do very badly in iterated scenarios.

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But this is not an iterated Prisoner's Dilemma. This is a one time multiplayer Parasite Dilemma. I designed it so that it has the flavor of an iterated Prisoner's Dilemma without the interations. So does your observation that pure parasite strategies do poorly in Iterated Prisoner's Dilemmas have any applicability to this one time Parasite Dilemma?

PairTheBoard

[PairTheBoard]

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If I feel everyone is going to contribute, why wouldnt I play parasite?


[/ QUOTE ]

Because of a reason you haven't thought of. A reason that depends on creative thinking. A reason that takes you outside your box of logic. A reason that the professional theoreticians are still working on formulating. A reason you will never discover unless you look for it.

PairTheBoard

[/ QUOTE ]


Can you enlighten us?

Or, is your answer, "you're wrong, but I just dont know why you're wrong"?

[/ QUOTE ]

I think it's an open question. I doubt I could present a theory that would stand up to the scrutiny of peer review by professional theoreticians. But I don't think the Nash Equilibrium I proposed and which Thylacine refined is the last word on the problem. From the Scientific American article it appears not to be the last word for the Traveler's Dilemma either. It's up to you if you want to participate in some creative thinking that goes beyond the theoretical status quo that many people think is inadequate for the analysis of this kind of problem.

If Thylacine's calculation is correct, everybody makes about $5 playing the Nash Equilibrium randomized choice. And if you are the only 100% contributor you make a few cents less. But suppose we postulate the possibility of the existence of a Super Rational process that goes beyond the logic of Nash. As a rational process it is one that everyone can arrive at independently and which everyone will act on, just as we now think they will act according to Nash's reasoning.

So here's an idea. Suppose we all postulate the existence of this Super Rational process without actually identifying it. What could we say about it? Clearly, it will be one that will make us more money than Nash's reasoning. We will all adopt it because it is rational and it will make all of us more money. Is there a choice for us that would satisfy that criteria? Yes. We all choose to cooperate. Does that universal choice make us all more money? Yes, we all make $100 instead of $5 apiece.

Why would you not then decide to go your own way and be a Parasite if everyone else is cooperating? Because the postulate is that cooperating is a Super-Rational Choice that overrides Nash reasoning and thus overrides your temptation to be a parasite. You participate in the Group Rational because it is superior to Nash reasoning for this kind of Dilemma. We all decide on this Super Rational Process and we all make money.

The more people who act on a Super Rational basis the more money everybody makes, including those who are unable to do so. So your choice is between being a Super Rational person who contributes to the common good or being a parasite. I think it's clear that the Super Rational thing to do is be a Contributor.

PairTheBoard

[Nicholasp27]

if u think at least 69 of the other players are 'super rational' then u should go parasite; it isn't rational, super or otherwise, to contribute if u know that the rest will contribute (which u are saying we will from this yet-undefined thought process)

[CallMeIshmael]

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Why would you not then decide to go your own way and be a Parasite if everyone else is cooperating? Because the postulate is that cooperating is a Super-Rational Choice that overrides Nash reasoning and thus overrides your temptation to be a parasite. You participate in the Group Rational because it is superior to Nash reasoning for this kind of Dilemma. We all decide on this Super Rational Process and we all make money.

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OK, I'll postulate a few things:

1. "I prefer more money to less money"
2. "I am one of the 100 players"
3. "I am 100% sure the other 99 players will play the superrational choice of cooperate"

Given the above, I can cooperate, and get $100 or be a parasite and get $194. Those are my two options (given the 100% certainty clause). You have the person choosing to cooperate. That is silly.


The error in your logic (and it is a common one) deals with a slight introduction of group thinking (specfically, the willingness to give up very slight bits of utility for yourself if it greatly benefits many others). To demonstrate the flaw, Ill ask you to think of a mind exereriment.

Imagine this scenario:

There are 100 animals in a tribe. For space reasons, 100, and only 100, in each year will survive. Each of the animals is either a contributor or a parasite. During each year, the animals play the game described in the OP. At the end of the year, animals are choosen at random to "reproduce," which will make up the next generation. Assume that the chances that the animal reproduces is proportional to the amount they made in the parasite dilemma game. (also, assume that there is some chance, say 10%, that a mutation occurs, and the offspring of a player switches to the opposing strategy).


(essentially, this is a model of evolution, in which the only gauge of fitness is the organisms strategy in the game).


What will happen?

Will the population find this so-callled "super rational" strategy?


(I bring this up, since evolution by natural selection is perhaps the best example of a situation where the small error you are making is most magnified.)

[PairTheBoard]

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it isn't rational, super or otherwise, to contribute if u know that the rest will contribute

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By definition, it is Super-Rational. Being Super-Rational makes everybody money. That's what makes it Super-Rational.

PairTheBoard

[Nicholasp27]

and if i go parasite against all the 'super rational' players, everyone will still make money, but i'll make more

what u are advocating is that everyone decides to go for top group gain rather than top personal gain

[CallMeIshmael]

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what u are advocating is that everyone decides to go for top group gain rather than top personal gain

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exactly


this isnt anything particularily new. You have just changed the payoff for each player from 'how much I get' to 'how much the average player gets.'

Once you do that, the nash equilbrium becomes, not suprisingly, to contribute.

[KipBond]

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it isn't rational, super or otherwise, to contribute if u know that the rest will contribute

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By definition, it is Super-Rational. Being Super-Rational makes everybody money. That's what makes it Super-Rational.

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I think the only way this can work, is if a player has some sort of utility outside of this one-time game. Perhaps "feeling good about not being a parasite" is worth more than he would gain if he were a parasite. Perhaps there is a meta-game where players learn about the other players' micro-game strategies, and adjust their behaviors accordingly. These sorts of things are what really happen in the real world.

My "Super Rational" strategy makes me feel good -- and when I talk to other people about their game strategies, if they aren't also a "super rational cooperator", then I don't trust them as much in other games.