From: ichudov@Algebra.COM (Igor Chudov @ home)
Date: Sat, 7 Jun 1997 15:14:54 +0800
To: mpd@netcom.com (Mike Duvos)
Subject: Re: Steak Knife Decryption
In-Reply-To: <199706070650.XAA22108@netcom19.netcom.com>
Message-ID: <199706070705.CAA00810@manifold.algebra.com>
MIME-Version: 1.0
Content-Type: text



Mike,

Thanks for an interesting reply.

What if, for example, the prisoner convinced the robbers that he
was irrational and would swear to God that he would never give up
his PIN. Assume that he made a very credible promise, ie, the victim
is a known nut. Assume also that the victim is also able to convince
the robbers that he would not tell anything to the police.

The robbers would then face a choice: whether to kill the victim
and face murder charges with punishment M and probability Pm, or
not to kill the victim and face charges R (for Robbery) with 
probability Pr. Since the victim is not going to tell anybody,
Pr is zero. So they now choose not to kill the victim.

How can this victim make a credible promise not to tell the
police?

I think that Jim Bell's assassination bot would solve this problem.
The victim would pledge $1,000,000 to the bot, with the instruction
to give it to the robbers if they are ever arrested within the statute
of limitations. After the statute expires, Jim Bell's bot would return 
the money back to the victim.

The AP bot could generally be a great tool for creating various
credible threats.

igor

Mike Duvos wrote:
> 
> 
> ichudov@algebra.com (Igor Chudov @ home) writes:
> 
>  > Mike Duvos wrote:
> 
>  >> An interesting twist on rubber hose decryption in the case
>  >> of the murder of Jonathan Levin, son of the top executive of
>  >> media giant Time Warner.
> 
>  >> Police believe his ATM card was stolen, and he was then
>  >> jabbed with a steak knife until he revealed the PIN.
> 
>  > This brings up a question. Did these robbers kill him right
>  > after they found out the answer, or they first tried to
>  > withdraw money to check if his number was right?
> 
>  > This brings up a question on the strategy in this game.
> 
>  > Suppose I am captured by ruthless robbers. They ask me for a
>  > number and torture me. They will torture me as long as
>  > necessary until I give out the correct number, and then
>  > they kill me.
> 
>  > Assuming that I am rational and prefer torture to death, I
>  > should not tell them the right number and delay the
>  > process, with the hope that possibly the police will come
>  > and rescue me.
> 
>  > Assuming that robbers are rational and know that I am
>  > rational, they certainly should not put me in such
>  > position: if they do, they are going to waste a lot of
>  > precious time and have no chance of getting the money.
> 
>  > So, they should promise me that they would not kill me.
> 
>  > But how would I believe them? A rational robber should kill
>  > the victim after she gets the money.
> 
>  > I am not quite clear if rational people can get something
>  > out of torturing other rational people. Maybe, I am
>  > confused and wrong somewhere.
> 
>  > Maybe, if the robber can convince the victim that she
>  > (robber) is irrational and would hold on to her promise not
>  > to kill him, she could get the money. But how to do that?
> 
> This is a kind of a Prisoner's Dilemma type game-theoretic
> problem. Each side desires to maximize their mathematical
> expectation, which is the sum of their expected return for each
> possible behavior of their opponent times the probability that
> behavior will occur.  One may assume that one has an intelligent
> opponent who can also analyze the game.
> 
> The robbers can either promise to let their victim live after the
> PIN has been extracted, or not.  Once torture has produced a PIN,
> and it has been tested in the ATM, they can either kill their
> victim or not kill him.
> 
> The victim can either give the PIN before major damage is done,
> or he can hold out until he either dies or rescue arrives.
> 
> For the robbers, the money is a small return, and getting charged
> with murder should the police arrive right after the victim has
> been terminated is a big loss.  Letting the victim live to
> identify the robbers is a medium sized loss, but killing the
> victim and getting away with it is no loss at all. For the
> victim, the loss of some money is a small loss, and the loss of
> ones life is a big loss.
> 
> Now the only return for the robbers is the money, so anything
> that doesn't result in the money is worse than not committing the
> crime in the first place.  There is no incentive for the robbers
> to say that they will kill you and not do it, so we can assume
> the robbers will not lie about this.  A rational victim will
> postphone death as long as possible, so it is always in the best
> interests of the robbers to say that they will not kill the
> victim.
> 
> This crime takes a very short amount of time to commit, so rescue
> is unlikely.  Torture which results in either the PIN or mortal
> injury can be carried out in under a minute.  If the PIN is not
> disclosed, death will therefore result.  If the pin is disclosed,
> you have a chance of living equal to the chance the robbers will
> not kill you.
> 
> So the optimum strategy if both players have analyzed the game is
> for the robbers to promise not to kill you, the victim to always
> immediately give up the PIN, and then for the robbers to either
> kill or not kill the victim, based on the relative penalty times
> the chance of getting caught for each alternative.
> 
> There is nothing the victim can do to improve his chances, except
> to hope he lives in a community where the penalty for robbery is
> small compared to the penalty for murder, and that a
> disproportionate amount of law enforcement resources are devoted
> to solving murders, versus solving robberies.
> 
> --
>      Mike Duvos         $    PGP 2.6 Public Key available     $
>      mpd@netcom.com     $    via Finger.                      $
> 



	- Igor.