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jrr, I also have a question about one of your early steps:

So #7 can offer the plan: "999 for me, 0 for #8, 1 for #9, none for #10." #8 votes in favor of the plan because it lets him live. #9 will vote in favor of the plan because he at least gets some gold out of it. #10 will vote against it, but it won't amount to anything. So #7 hopes things will get to step 7! He can win if he gets there!

This situation comes up a lot in tax and estate planning. "If we (7 and 9) cooperate, then we can split $1000 in tax savings - if we don't cooperate, the IRS (10) gets all of it."

In my experience, the guy who has more leverage gets the bulk of the money. Here, 9 has more leverage because 7 is certain to die if 9 votes against, but 9 may not die if he and 10 are left.

So if 9 says to 7, "Give me $999 or I'm voting against you," wouldn't a rational 7 give it to 9 rather than dying to spite 9?

I'm probably making this way more complicated than it needs to be.

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