Re: Twenty Bank Robbers -- Game theory:)

[John Brothers <johnbr@atl.mindspring.com>]

At 07:19 AM 7/26/96 -0400, you wrote:
>On the other hand, a proposal by the first guy to split the
>proceeds equally among the first ten should be satisfactory to the first
>ten.  On that basis nobody dies and ten receive two million each, if we
>assume that each is a simple profit maximizer.
>
>I think that that result is stable, but am not going to try to prove
>that it is.  (If the result is not stable, it should be relatively easy
>to establish that fact.)

Slightly more stable is:  punk #1 proposes that punks 2 - 10 get all the 
money, and he gets none, if he prefers poverty to death.  Now, why does this
work?

Punk #1 has set a precedent that improves the share of each of the following
9 cypherpunks by 11% over the 'first 10 split evenly' proposal, to 2.22 million.

In order to justify killing punk #1, according to the rules, punk #2 will
have to come up with a proposal that improves his share to more than 2.22 
million (because the cypherpunks don't want to kill each other unless there
is more money to be made)

But he can't - there are still 18 other punks left, and he'll still need 9
additional votes on his side to stay alive - and he'll die if he gives less
money to the 'lucky 9' than #1's proposal, since everyone can see that as
more people die, the total profit available to the remainder will increase.

In other words, if he votes no, he will be forced to offer 2.22 million to
punks 3 - 11, to stay alive, and take no money himself.  He loses by voting
no, so he is a guaranteed yes.

Punk #3 will consider voting no.  Since there will only be 18 left when he
gets the proposal, he can also propose 2.22 million to punks 3 - 11.  But
a) he can't do better than 2.22 million, and that means that he has to vote
yes, since he doesn't want to kill the other punks, everything else being
equal.

Punk 4 is in the exact same situation - with 17 left, he still needs 9 to
win, and voting 2.22 million to punks 4 - 12 won't gain him anything over
voting yes.  So he will vote yes because he doesn't want to kill.

Punk 5 is the first one with a chance at a windfall.  If he bumps off 1 - 4
he can propose 2.5 million for himself and 6-12.   But he is vulnerable to
the same strategy from punk #7.  7 will have no reason to keep #5 alive, since
that will reduce his profit margin.  #5 will be forced to vote yes to stay
alive.

#6 is in the same situation as number 5, since he can't increase the profit
margin.  He has to vote yes

#7 is vulnerable to #9.  8 has no advantage, they both vote yes.

#9 is vulnerable to 11, and 10 has no advantage.  They both vote yes, and
that is it.

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John Brothers 
   Do you have a right not to be offended?