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Not necessarily. If it so happens that #n+1's plan will be accepted and leave #10 with zero, then #10 will vote in favor of #n's plan as long as it leaves #10 with some money.

I see what you're saying, but I think you have to know how risk averse the players are. Given the uncertainties, I'm not sure that you can ever say with certainty that n+1's plan will definitely be accepted. For instance, what if one of the high-number players decides to give up a certain but negligible payoff in the hope that it will come down to them and they'll get it all? They might be willing to come out a little less rich because they want the chance of the big score.

The payoffs are high enough that one's risk aversion plays a big role, unless you assume that everyone's risk neutral. I didn't see that assumption in the problem.

Another thing: if they collude, they can reduce some of these risks. But I'm not sure what the rigid solution to the collusion negotiations might be.

dan
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