Comment author:Zack_M_Davis
22 November 2013 03:34:59AM
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22 points
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For the Prize Question, you should use a random number generator and cooperate with probability 0.8. Why? Suppose that the fraction of survey-takers that cooperate is p. Then the value of the prize will be proportional to p and there will be p + 4(1 - p) raffle entries. The expected value of Cooperating is p/(p + 4(1-p)) and the expected value of Defecting is 4(1-p)/(p + 4(1-p)). In equilibrium, these must be the same: if one choice were more profitable than the other, then people would switch until this was no longer the case. Thus p = 4(1 - p) and thus p = 4/5.
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For the Prize Question, you should use a random number generator and cooperate with probability 0.8. Why? Suppose that the fraction of survey-takers that cooperate is p. Then the value of the prize will be proportional to p and there will be p + 4(1 - p) raffle entries. The expected value of Cooperating is p/(p + 4(1-p)) and the expected value of Defecting is 4(1-p)/(p + 4(1-p)). In equilibrium, these must be the same: if one choice were more profitable than the other, then people would switch until this was no longer the case. Thus p = 4(1 - p) and thus p = 4/5.
Addendum 29 November: Actually, this is wrong; see ensuing discussion.
I think that way to get maximum reward is doing the survey (at least) four times and always answering cooperate.