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!