From: Jeremey Barrett <jeremey@forequest.com>
Date: Fri, 26 Jul 1996 10:24:01 +0800
To: Igor Chudov <ichudov@algebra.com>
Subject: Re: Twenty Bank Robbers -- CLARIFICATION
In-Reply-To: <199607251813.NAA02650@galaxy.galstar.com>
Message-ID: <Pine.BSI.3.93.960725162632.2394B-100000@descartes.forequest.com>
MIME-Version: 1.0
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Assuming "perfect" intelligence on the part of the robbers (i.e. they will
follow deterministic behavior and do the "right" thing), then here's what
must happen IMO (1 being the first guy and 20 being the last):

1 must propose that 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 all split
the money evenly. All of these will vote for it, assuming they're all
perfectly smart and deduce the inevitable outcome.

I arrived at this working backward from the case where two robbers are left.

If 2 are left (19 & 20), 19 gets all the money. So 20 will vote for whatever
18 says, which MUST include 20 in the deal. Since 19 knows this, 19
will vote for whatever 17 says, which must include 19 in the deal, and so
forth. Eventually you arrive at the conclusion that 1,3,5...,19 must
all agree to split the money at the beginning.


On Thu, 25 Jul 1996, Igor Chudov wrote:

> 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?
> > 
> 
> I forgot to say what the GOALS are. The goals of every individual
> cypherpunk are (in from highest to lowest priority): 
> 
> 1. Stay alive
> 2. Get as much money as possible
> 3. Keep as many cypherpunks alive as possible, all other things being equal.
> 
> 	- Igor.
> 

- -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Jeremey Barrett
Senior Software Engineer			jeremey@forequest.com 
The ForeQuest Company       			http://www.forequest.com/

   "less is more."
		-- Mies van de Rohe.

   Ken Thompson has an automobile which he helped design.  Unlike most
   automobiles, it has neither speedometer, nor gas gage, nor any of the
   numerous idiot lights which plague the modern driver.  Rather, if the
   driver makes any mistake, a giant "?" lights up in the center of the
   dashboard.  "The experienced driver", he says, "will usually know
   what's wrong."

		-- 'fortune` output

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