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Spieltheorie - Gefangenendilemma
Freigegeben von: Wolfgang Melchior
Spieltheorie (Game Theory)

Spieltheorie umfasst ein weit größeres Gebiet als nur die Behandlung des Gefangenendilemmas. Zwei Namen sind untrennbar mit ihrer Entstehung verbunden: John von Neumann und Oskar Morgenstern mit in ihrem 1944 erschienenen Buch „Theory of Games and Economic Behavior“. Darin wurde zum ersten Mal ein Modell einer Entscheidungstheorie auf mathematischer Basis entworfen. Dabei wurden die Entscheidungen der „Spieler“ als eine rationale Wahl von zu erwartenden Ergebnissen (outcomes) verschiedener Alternativen (sog. lotteries) aufgefasst. Interessant waren die Spiele, in denen mehrere (meist zwei) Spieler verschiedenen Strategien ihrer Nutzenmaximierung verfolgen. Von Mathematikern formuliert und als Disziplin der Wirtschaftswissenschaften zuhause (Selten, Maynard, Harsanyi, Nash), wurde erst mit der Diskussion des Gefangenendilemmas die sehr technische Diskussion der Spieltheorie auch für Soziologen, Politologen und Philosophen interessant.

Im Folgenden könnt ihr einen Artikel eines unbekannten Autors zum Gefangendilemma studieren.


[Weitere Links zur Spieltheorie] [Download Demoprogramm zum Gefangenendilemma in QBaisc]


Prisoner's dilemma


In The Wealth of Nations Adam Smith postulated an 'invisible
hand' that would lead individuals to further the common interest
through the pursuit of their own self-interest. One problem for
social theorists, economists and moral philosophers has been that
this happy congruence between individual and collective interest
often fails to occur. Anyone who has been stuck at a busy junction
when traffic lights fail will know that the pursuit of self-interest
by each, doesn't bring about a better situation than when the pursuit
of self-interest is regulated and controlled. One type of situation
which illustrates this is the so-called Prisoner's Dilemma.





Imagine two prisoners called Cain and Abel. They have just been
arrested by the police who suspect them of a bank robbery but can
only prove the charge of shoplifting. The investigating officer,
having placed the two criminals in separate cells, approaches Cain
with a deal. 'If you give evidence against Abel for the bank job,
then I'll grant you immunity on all charges, unless he also gives
evidence against you (and I'm offering him a similar deal) in which
case I'll proceed against you both on all charges.' What is Cain to
do? Clearly the best outcome for Cain is one where he gets off
scot-free by denouncing Abel. He knows the best outcome for Abel is
one where Abel escaped prosecution by denouncing him. It
would be a good idea to find some way of securing Abel's co-operation
and keeping quiet, but this he has no way of doing. If he refuses to
grass on Abel then there is every prospect that Abel will take him
for a sucker. The result: both confess and bring about a situation
that is worse for themselves than if both had kept quiet. This is
can be represented in a diagram where the number on the left of each
pair represents years in prison for Abel and that on the right years
in prison for Cain:

                       
CAIN
not confess confess
ABEL not confess 2, 2 11, 0
confess 0, 11 10, 10



We can make the problem more general by using not years of a sentence
but simply ranking of possible outcomes for each 'player':




CAIN
not confess confess
(co-operate) (defect)

ABEL not confess OK, OK worst, best
(co-operate)
confess best, worst bad, bad
(defect)



There is a slight tension between the terminology of the employed in
the story from which the prisoner's dilemma derives its name and the
terms normally used in game theory: the prisoner who does not
confess is said to be co-operating (with his fellow
prisoner) and the one that confesses is said to be defecting.
In a single game between two players the equilibrium is mutual
defection, bringing about a suboptimal outcome since there is
an alternative where both players do better. If defection is always
the best thing to do if two players play the game once, does it
follow that the best strategy to adopt if the same two players
play the game many times is 'always defect' ? The answer is no. Two
players can use patterns of defection and co-operation to secure
conditional co-operation (I will if you will). In an iterated
prisoner's dilemma
the best thing to do is to co-operate at
first, but then to respond by copying the other player's previous
move. If you co-operate with me, then I'll co-operate with me, but if
you seek to exploit me by defecting then I'll retaliate in the next
game. Thissimple tit-for-tat strategy does better for those
that employ it in iterated games than any other. In many situations
of repeated encounters between people, playing the 'tit for tat'
strategy means that rational self-interested people will act as if
they are motivated by moral concerns even though they really only
care about themselves. Thus, to steal an example from Kant, a
shopkeeper may refrain from cheating his customers because a
reputation for honesty will secure their business in future rather
than out of a sense of moral duty.


A puzzle: tit for tat may work best in repeated games, but does it
determine what it is rational to do? Every sequence of games comes to
an end and surely the right thing to do in the last game is to defect
since there is no next game in which to suffer the consequences. If
this is the right thing to do in the final game, then shouln't I
steal a march on my opponent by defecting in the penultimate one?
And how about the one before that....?


Further reading: Robert Axelrod, The Evolution of Co-operation
(Penguin).

 
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Spieltheorie - Gefangenendilemma


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