Re: Twenty Bank Robbers -- Game theory:)

[Rabid Wombat <wombat@mcfeely.bsfs.org>]

On Thu, 25 Jul 1996, Marshall Clow 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?
> >
> It seems to me that the last two guys in line will _almost always_ vote for killing the suggestor.
> 
> the exceptions being for extreme suggestions like "let's split the money between #19 and #20", which I figure will get voted down by #s 2 thru 18.

Starting at the end, and working to the beginning:

If only 19 and 20 are left, 19 has 50% of the vote, and can take all. #20 
loses out.

Therefore, with 18,19, and 20 left, 20 will take whatever 18 offers, as 
it is better than getting nothing.

With 17,18,19,20 left, 17 should propose a split with 20, who will likely 
get a smaller cut from 18, because of the above.

With 16, 17, 18, 19, 20, three votes are needed, reducing the take for 
the majority, so no one other than #16 is acting in their best interest 
to approve a split, except for #19 trying to avoid losing out to 17/20 in 
the next round. Not enough for a majority.

Follow this forward, and find that any even numbered cypherpunk on 
Ritalin with UZI bankrobber is useless, as an additional person is needed 
to form the 50%-or-better as compared to the next round.

All even-numbered cypherpunks should then expect a short life expectancy. 
(You are number 6; who is number 1?)

Therefore, punk #2 should propose that the money be split equally between 
all even-numbered / disadvantaged punks, as they will otherwise all get 
bumped off by odd punks. The odd punks, of course, get nothing in #2's 
proposal.

Taking this one step further, and assuming that all clever punks have 
realized this, punk #1 proposes that the evens will perform the above 
split, if #2 is allowed to advancve this proposal, and therefore the only 
profitable option open to odd punks is to spilt the money between 
themselves, giving the even punks nothing.

Of course, if one of the punks is our recently arrived ^h^h^h^h
(just remembered I'd taken the pledge ...)  ;)

Rabid Wombat
Nocturnal Diseased Marsupial

The moral of this story is that it is good to be an odd punk ...

> 
> -- Marshall
> 
> Marshall Clow     Aladdin Systems   <mailto:mclow@mailhost2.csusm.edu>
> 
> "We're not gonna take it/Never did and never will
> We're not gonna take it/Gonna break it, gonna shake it,
> let's forget it better still" -- The Who, "Tommy"
> 
> 
>