From: Hal <hfinney@shell.portal.com>
Date: Sat, 27 Jul 1996 06:45:40 +0800
To: cypherpunks@toad.com
Subject: Re: Twenty Bank Robbers -- Game theory:)
In-Reply-To: <v03007805ae1e24c262c7@[192.187.162.15]>
Message-ID: <199607261724.KAA16957@jobe.shell.portal.com>
MIME-Version: 1.0
Content-Type: text/plain


Gary Howland <gary@systemics.com> writes:
>I think many are assuming that the cypherpunk making the suggestion
>gets a vote.  My reading of the puzzle is that he does not.

As we have seen apparently the intention was that he does get a vote.
However I don't think the answer changes even with Gary's interpretation.

With two people, #1 (the front of the line) must propose that all money
go to #2, otherwise #2 (who is the only one with a vote in Gary's
version) will vote against it (and get all the money when #1 dies).
With this proposal #2 will vote in favor since he gets the same amount
of money either way, and it keeps more people alive (see the post which
describes the goals of the robbers).  This is different than the
original problem, but it is the only case which differs.

With three people, #1 (in front) proposes to keep it all.  #2 will vote
in favor since if the proposal doesn't pass, #2 will end up with nothing
anyway (per above).  So #2's third goal comes into play, maximizing the
number of players alive, and he will vote in favor.  #3 may vote
against but #2's vote will be 50% (#2 and #3 get to vote in Gary's
version) and will carry.  So #1 keeps it all, the same answer as in the
original version.  Extensions to n players are again left as an exercise,
but I think the answers come out the same in Gary's version.

Hal