Let's talk Itsuki and his Legion strategy.
When I just started reading Comyu, I found this line to be quite striking -- so much that I made a post about it here. The reason I found this striking was that Itsuki was referencing a real 'tournament' of strategies for the Prisoner's Dilemma--known as Axelrod's Tournaments--and was almost entirely correct. Very importantly, the strategy that came on top is indeed the very same strategy Itsuki described, known as tit-for-tat.
I quickly started identifying Itsuki's strategy with tit-for-tat, and there were a few very nice parallels. I will first describe the strategy and the tournament itself.
AI strategies compete against each other in rounds of the Prisoner's Dilemma, where they know who they are playing against and may choose to either Defect or Cooperate. This tournament took place twice and with slightly different rules: for the first tournament, each strategy played every other strategy (including itself) exactly 200 times, and the second tournament had the strategies play approximately 200 times (game ends depending on probability).
The reason for that change is that this form of Prisoner's Dilemma has a theoretical 'disadvantage' if the exact number of games is known that makes defection even more attractive than it already is.
In both tournaments, tit-for-tat came out on top. In addition to that, there was also a tournament variant where the strategies were allowed to replicate based on their score. This variant also had tit-for-tat come out on top, but only under the caveat that most of the population was not currently the always defect strategy (in which case tit-for-tat became extinct).
When making the analogy between this tournament and Comyu, I consider one Comyu attacking another to be a 'defection', and not attacking to be 'cooperation'. For cases where Comyus team up, I will consider it as one Comyu adopting each other's strategy -- since we haven't really seen any BKs fighting other BKs or a fight break out within the Legion.
I'll come back to this after a brief description of tit-for-tat and its key attributes.
The tit-for-tat strategy is very simple. Here is how it works:
That's it. Like Itsuki said, tit-for-tat exacts proportional retribution, without excess and without hatred. Another key point that Itsuki may have neglected to mention was that tit-for-tat is never the first to defect. This might sound trivial, but when two tit-for-tat strategies meet, they will cooperate forever. However if aggressive-tit-for-tat strategies meet, they will never break the cycle of retribution.
The reason tit-for-tat failed in the population-based tournament when there were too many always defect strategies was that its initial niceness on the first turn gave it a small disadvantage that, since always defect never changes its behavior, it could never recover from.
Another weakness of tit-for-tat is the subject of noise. That is, if tit-for-tat thinks it was betrayed, it will exact retribution. It will not pause to think. This might not sound like a huge problem, but remember that if two tit-for-tat strategies are playing against each other and one of them defects, the defections will never end past that point; each round, one strategy will cooperate and the other will defect, and on the next turn they will alternate.
Okay, having finished this introduction, let's go back to Comyu and Itsuki. Throughout the novel we never see Itsuki initiate the first attack on anyone -- the most he does is grow at a very high rate and threaten to take over or replace the Round Table -- which is just equivalent to his strategy replicating due to being successful.
But notice that once the Comyunet gets into an open warfare situation (that is, everyone starts defecting), Itsuki's tit-for-tat falls apart and he dies. His avatar may have beaten many other opponents, which might symbolize Itsuki's currently high aggregate score being higher even after many defections, but he cannot sustain this.
It might be possible to consider Rondo Rondo (sadly not Noiz) as the threat of noise to Itsuki, which wasn't enough to wipe him out completely much like how a single error in tit-for-tat doesn't result in infinite defection from both sides at every single round. This part could be a bit of a stretch though.
Unfortunately, this is about as far as my analysis goes. We haven't seen that much of Itsuki's actions and tactics so there is only a limited amount of material to analyze. I also haven't been able to find a Prisoner's Dilemma strategy that fits with another Comyu as neatly as it does with Itsuki. The Round Table might be a more forgiving tit-for-tat variant that exacts retribution once for every two defections, which is very peaceful but also pretty weak.
Akihito's strategy might be considered random. He can't be tit-for-tat because he willingly gets into fights that aren't his, and he is clearly neither always defect nor always cooperate. My memory of Comyu isn't perfect, but maybe the feminist strategy can be defined like this:
(It's true that Akihito did have that first fight with Nanase, but since Akihito was opposed to that battle as far as I remember, so I'm giving him a pass.)
