The
Shadow Of The Future
I have above described many
dilemma strategies; AD (Iron rule), AC (Gold rule), TFT (Silver rule), R, RTFT,
and Pavlov.
R is an attempt to combine AC
with AD; however, it shares an important characteristic with them; it is
“unresponsive” (i.e. it does not reward the other’s nice behavior with nice
behavior of its own) and it is “unirritable” (i.e. it does not punish the
other’s mean behavior with mean behavior of its own).
Responsiveness and irritability
are part of the definition of life; thus AD, AC, and R are all “dead”
strategies, unlike TFT, which is “live”. There is no point in being nice to a
dead strategy; you cannot reform it if it is bad, or anger it if it is good.
Conversely there is no point in being mean to a live strategy, for your
misbehavior will only backfire on you. Therefore: be nice to the living and
mean to the dead!
TFT is a live strategy (i.e.
irritable and responsive), a nice strategy (i.e. it never defects first), and a
simple strategy (thus easily identified as such by other strategies); these
qualities combine to give TFT unique advantages in dilemma play. Robert
Axelrod, in his book The Evolution Of Cooperation, reports that in two
open-invitation computer tournaments, TFT came out ahead twice.
In Appendix B of that book,
Axelrod was able to prove that TFT is a dominant stable strategy, if the
“shadow of the future” is large enough. This is the “Axelrod equilibrium”;
reciprocity can and does keep the peace, in the long run, provided that the
long run is long enough.
The shadow of the future looms
large over everyone’s calculations. Tit-for-tat (which mandates cooperation on
the first move and reciprocation thereafter) is optimal if w exceeds both (W-T)/(W-D) and (W-T)/(T-L). Above the transition
probability, the shadow of the future exceeds both (W-D)/(T-D) and (T-L)/(T-D).
It is probably most interesting
to run a tournament at the transition probability; for there the Iron
Rule meets the Silver Rule head on. Here are some tables of various dilemma
scoring systems, and their correspond transition probabilities, times, and
recommended randomizing devices:
L
D T W t.
prob. t. time randomizer
“Army”: 0
1 2 3 1/2
2 rounds coin
“Navy”: -3 -1 1 3
1/2 2 rounds coin
0
1 3 4 1/3
3/2 rounds roll
< 2
-2 -1 1 2 1/3
3/2 rounds roll
< 2
Below the ‘transition
probability’, Iron rules; above the transition probability, reason favors
Silver sweetened by a bit of Gold. After the ‘transition time’, mutual
exploitation gives way to a kinder and gentler society.
A shadow is haunting Earth; the
shadow of the future. Will we be or will we not be? That is the question; for
justice will prevail, but only in the long run. You should live so long!
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