In the meantime I’ve run my own simulation, studying a group of strategies, which perform as tit-for-tat except that at specific turn they defect and then they use result of this turn to switch to defect stone or continue tit-for-tatting. Thus they recognize copies of itself and cooperate with them. Such strategy can be exploited by switching to defect stone before it does, or by mimicking its behavior (second defect check after first. This case I didn’t analyze).
It leads to interesting results in evolutionary tournament. Second fairest (second longest period of tit-for-tatting) strategy wins. It outperforms less fair strategies by longest cooperation with fairest strategy. And it outperforms fairest strategy by exploiting it.
Define strategy S[n] as TfT until turn n and defect ever since. In the limit of infinite population having non-zero initial number of S[n] for each n, S[0], i.e. DefectBot, eventually dominates. Starting with equal subpopulations, initially most successful is S[99] which preys on S[100] and finally drives it to extinction. But then, S[98] gains advantage over S[99] and so on.
With not so big population however, the more defectorish strategies die out sooner than the environment becomes suitable for them. (I have done it with population of 2000 strategies and the lowest surviving after several hundred generations was S[80] or so).
Try another strategy. I[n] - TfT until turn n, defect on turn n, on later turns check if result on turn n was (defect,defect) and play TfT, otherwise defect. Idea is selfcooperation.
In the meantime I’ve run my own simulation, studying a group of strategies, which perform as tit-for-tat except that at specific turn they defect and then they use result of this turn to switch to defect stone or continue tit-for-tatting. Thus they recognize copies of itself and cooperate with them. Such strategy can be exploited by switching to defect stone before it does, or by mimicking its behavior (second defect check after first. This case I didn’t analyze).
It leads to interesting results in evolutionary tournament. Second fairest (second longest period of tit-for-tatting) strategy wins. It outperforms less fair strategies by longest cooperation with fairest strategy. And it outperforms fairest strategy by exploiting it.
Define strategy S[n] as TfT until turn n and defect ever since. In the limit of infinite population having non-zero initial number of S[n] for each n, S[0], i.e. DefectBot, eventually dominates. Starting with equal subpopulations, initially most successful is S[99] which preys on S[100] and finally drives it to extinction. But then, S[98] gains advantage over S[99] and so on.
With not so big population however, the more defectorish strategies die out sooner than the environment becomes suitable for them. (I have done it with population of 2000 strategies and the lowest surviving after several hundred generations was S[80] or so).
Try another strategy. I[n] - TfT until turn n, defect on turn n, on later turns check if result on turn n was (defect,defect) and play TfT, otherwise defect. Idea is selfcooperation.
Except that in the initial state S[0] will get driven to extinction long before s[100] will.
With reasonably sized population, yes. In the limit of infinite population, or with sufficiently large population, no.