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.