Re: Twenty Bank Robbers -- Game theory:)

["Robert A. Rosenberg" <hal9001@panix.com>]

At 9:09 -0500 7/25/96, Igor Chudov wrote:


>Here's a puzzle for our game theorists.
>
>Twenty cypherpunks robbed a bank. They took 20 million bucks. Here's
>how they plan to split the money: they stay in line, and the first guy
>suggests how to split the money. Then they vote on his suggestion. If
>50% or more vote for his proposal, his suggestion is adopted.
>
>Otherwise they kill the  first robber and now it is the turn of guy #2
>to make another splitting proposal. Same voting rules apply.
>
>The question is, what will be the outcome? How will they split the
>money, how many robbers will be dead, and so on?
>
>igor

I've read the differing scenarios and they seem to fall into two groups -
Either #1 makes an offer good enough to get 9 others to vote for it (and
thus save his life) or there is a blood bath ending with #19 getting all
the money and #20 with nothing but his life.

I think that if the blood bath occurs it will not get to the 2 survivor
stage. I think it will end at the 4 (or possibly 3) survivor stage. I base
this analysis on #20's best outcomes and interests. He will survive no
matter what (assuming that we ignore the cases where those who do not get
their fair share wack those who got money and take it) so this is not an
issue for him (he has no way of being killed for being too greedy). The
amount of money that he will get is totally dependent on what the current
"split proposer" offers him as an incentive to vote for the split (as
noted, once #19 gets to the top of the queue, he can [will?] grab
everything and cut out #20 so it is in #20's financial interest to vote for
a prior robber who will offer him some of the money). Since the vote must
be 50% or better for the proposed split, once it is #17's chance (ie: When
we are down to only 4 robbers and 2 yes votes will "win"), he can get #20's
vote by offering him at least 50% of the money (more than 50% will be an
incentive to #20 to take the deal since if he goes thumbs down to a 50/50
split with #17, #18 will only need to offer #20 the same 50/50 deal ["its
then 50% or nothing"] after #17 gets killed). #17 can hedge his bet by
offering #18 some of the rest (assuming a secret vote or all voting at the
same time in ignorance of how the other voted) since it might gain his vote
(a split between 17&20 leaves #18 out in the cold so he might go for some
money as opposed to none [in the case where #20 goes for 17&20 split]).