Re: Twenty Bank Robbers -- Game theory:)

[David Sternlight <david@sternlight.com>]

At 3:55 PM -0700 7/25/96, Erle Greer wrote:
>At 09:09 AM 7/25/96 -0500, you 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
>>
>
>Here's my guess:
>Eache robber is going to want the largest share of the money possible.
>Therefore The first guy dies automatically because that increases the share
>size.  This continues on until there are only two robbers left.  Robber #19
>suggests that he receives the full 20 million and since his vote is 50%, he
>receives it all.  18 robbers dead.

No. Robber 18 knows that he will be killed under those circumstances, so he
proposes that Robber 20 gets all the money. 20 votes with him. Now iterate
backwards. If, under my assumption the proposers are selected by lot at
each stage, then 18 still knows he'd be killed, but not knowing which of 19
or 20 is the next proposer, suggests 19 and 20 split 50-50. Since each
knows that he might be #20 and get nothing on the next round, they accept.
Now iterate that one backwards.

David