From: JR@ns.cnb.uam.es
Date: Mon, 29 Jul 1996 20:50:15 +0800
To: cypherpunks@toad.com
Subject: Re: Twenty Bank Robbers -- CLARIFICATION
Message-ID: <960729114511.2080086f@ROCK.CNB.UAM.ES>
MIME-Version: 1.0
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> 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.
> 

	Most responses fail to consider "suicidal" behaviours. In many
cases, when there are rounds left, it may be worth playing against your
interests if that will yield later a higher benefit.

	The fact that anyone makes a proposal is of no interest to anyone
else as long as goal#2 stands over goal#3 and there is enough people to
stablish uncertainty of behaviour.

	As an example, if #1 proposes he gets all the money, all other
things being equal, #3,#5,...#19 should theoretically vote for him since
they know they can't win as long as there's a #2...

	But #19 knows he could win if only he and #20 were alive. It is
in his interest to vote 'no'. If #1 dies, then he may get a chance, because
#18 is in his same position and might do the same in the other rounds. Yes,
you can follow it backwards and discover that goal #3 above then should
take precedence. Should it?

	There's still goal #2 above. If the c'punks can't communicate 
among them then that's the end of it. #1 gets all. But if they can, 
there's another side:

	If you not only know the order of proposers, but also their
proposals, then you can always play 'unfair' or 'against you' until the
proposal that's better for you comes. Say #2 speaks to #20 and agrees to
propose that he'll get some money too. Restriction #2 above takes
precedence and proposer #2 knows he'll get #20 vote as long as he makes
that proposal. It is in #20's interest to vote against #1 "all for me" in 
the first round since that way he'll get some money on #2's proposal.

	But then #3, #4, etc... can play the same game. The first one that
can provide a proposal making happier most of the people will win...

	Say #1 proposes to even split between half of them. Will that work?
If they can't cheat their vote that's the end of it. Then comes another
point in place. Can they cheat?

	Obviously, under these arrangements, anyone proposing he gets all
money, other than #19 risks his life for others can agree into a better
split. But OTOH, #18 and #20 know that they can agree on something better
than #19's proposal of he getting all. If #18 cheats, #19 can agree with
#20 to split even and #18 is dead. If #18 doesn't cheat. then #20 has
two chices:

	- believe #19 will not cheat and propose an even split. Vote against.
	- fear #19 cheating and the risk of not getting anything. Odds are
all for #19, so he shoudl vote for #18 proposal.

	The only choice is for #18 and #20 to agree in an even split, where
#18 can also cheat and ask for all money. But then he risks #19 and #20 
agreeing on voting against him. So #18 must offer something to #20, and it
must be enough for #20 not wanting to take the risk of #19 cheating too.

	Following back, everybody but #19 and #20 risk their lives. #19 is
interested in everybody else being dead, and #20 in anyone giving him
anything. Anyone who gives anything to #20 will get his vote. Anyone not
giving anything to #20 risks #20 voting for someone else on the hope he'll
get something on the next proposal. And everyone needs an agreement with
#20 to keep his life.

	As you go back, #18 has a better chance of staying alive if he can
ensure #19 and #20 won't agree because his offer is safer than the risks
involved for #20. Work backwards.

	The point is, the expectancies of winning work at all round, and at
every point you are interested in not dying. As you reach the end if you
make an agreement and cheat you have less risk (there are less possibilities
for new agreements), but if you have gone to that, it's because more and
more people have cheated before, and confidence will be low. So you are
more interested in not cheating to keep your life.

	I think the net result is that most c'punks will be offering 
even splits to ensure a maximum of votes. As people makes arrangements and
c'punks dies, confidence and credibility on agreements in advance will
fail, so the risk for the latests increases too...

	In the end all comes down to gullibility of the partners. If you
assume they are not gullible, you'll vote for the first proposal of an
even split to save your life. If they are, then you can play against
while there remains gullible people, but then you know your cheating is
your dead (except for #19 and #20) and you risk less by going even.

	That's more or less like real life: one can temporarily play
against himself if that will yield later a higher benefit. But that
comes at a cost in credibility, and the more you use it, the less useful
it becomes.

	On a non-gullible environment, the first time you cheat your
reputation breaks and it is in everyone else's interest to play against
you. That's the ancient concept of honor. On a less-exceptic or more
tolerant environment you may have a few goes before getting people
absolutely exceptical again. The number of goes will depend on their
tolerance level.

	Same for the game: there can be cheating up to a tolerance level.
After that everyone will know that a non-even split proposal will take out 
your life. Where the border comes is a matter of circumstances.

				jr