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.