Re: Steak Knife Decryption

[mpd@netcom.com (Mike Duvos)]

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.                      $