From: Brett Paatsch (paatschb@ocean.com.au)
Date: Tue Feb 25 2003 - 04:01:36 MST
It goes like this.....
------------------------------------------------------
A traveller "X" wants to get to St Ives and arrives at a T intersection
(see Fig A. below) at which stand two "custodians of the pass"
"O" and "O".
(path 1) <-----------------------------> (path 2)
O | O
(custodian C1) | (custodian C2)
|
|
X (the traveller)
(Fig. A.)
[How things *look* to traveller X approaching the T intersection
with two "custodians" and two possible paths. ]
Traveller X has been reliable informed that the correct path
to St Ives can be taken by either turning left or turning right
but he has not been told which.
Traveller X knows that one of the custodians of the pass
will always respond to questions with a lie and the other
will always respond with the truth. Both of these custodians
know each other well and both know the actual way to
St. Ives. T does not know which custodian is the liar and
which is the truth teller.
He is permitted only one question to one of them to determine
the way to St Ives. But one question is enough.
What is the question?.
(answer at bottom of the post just in case anyone doesn't
know and wants to try and work it out themselves)
Fig B. Shows the truth that Traveller X can't "see".
(path 1 is .... ( path 2 is....
the way to St. Ives) <---------- ---------> NOT the way)
O | O
(C1 always tells the truth) | (C2 always lies)
|
X
Figure B.
-----------------
[The answer:]
Traveller X can ask either custodian "which way would
he (the other custodian) have told me to go if I had
asked him the way to St Ives.
Then Traveller X knows the way is the opposite.
Traveller X still does not know if he spoke to the liar
or the truth teller and he doesn't care as he is already
on his way to St Ives.
-----------
Lee is quite reasonably sceptical about the use of the
term "game theory" in relation to the Iraqi crisis.
I applaud that scepticism, and if I can explain my "reasoning",
without losing too much time I'd like to give it a shot. In
some ways its easier to just give "the answers" and not "the
method". The answers should be testable, and challengeable
themselves even if the method is not. (The first "answer" was
that Bush should approach Chirac and ask him to come
up with a standard of proof to be applied generally by the
Security Council in order to decide whether a particular
go-to-war decision was warranted. This answer has the
appeal of preserving the UN and affixing accountability for
failure and of making poor faith or poor judgement
apparent - I think).
I don't know if the above problem is really about "game
theory" per se. But the phenomenon that is that problem and
Axelrods "discovery" that the principles of tit for tat are
teachable and once learnt constitute a strategy that cannot be
beaten in iterative prisoners games even by those who know
they are playing against it has certainly influenced my sense
that the current Iraq crisis and the "standoff" within the UN
is rationally resolvable despite human passions.
I don't know that what I am actually doing is game theory with
capital letters. I think what I am doing is trying to come up with
a set of rules or a procedure which is guaranteed to give the best
possible outcome given certain facts and given that those facts
can be presented to free agents who have choice but who are
bounded to act in the social world in only finite and limited ways.
Perhaps rather than game theory I am doing a sort of transaction
analysis.
Maybe I'm just being a w**ker. But if so I am not being so
knowingly.
Regards,
Brett
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