Twenty Bank Robbers -- Game theory:)

[Peter D. Junger]

Erle Greer writes:

: 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.

That ``solution'' assumes that cypherpunks are rather stupid.  Since
everyone can do that calculation it is quite clear that at least 18
would refuse to vote (or fail to vote) in a way that produces such a
result.  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.)

--
Peter D. Junger--Case Western Reserve University Law School--Cleveland, OH
Internet:  junger at pdj2-ra.f-remote.cwru.edu    junger at samsara.law.cwru.edu