I played this a little while ago and it was pretty cool, and obviously makes a good point. I did have one issue with it though...
The game only considers a small finite set of strategies, from which the best performing strategy against the others over time was the "cheat only after you're pretty sure that you're opponent is a cheater" strategy. The game makes it seem like that strategy is some sort of "long term equilibrium". And I'm sure that in the real world where we play similar games, it may be. But for this specific game, it isn't actually. The rules of the game state:
you'll play anywhere between 3 to 7 rounds. (You won't know in advance when the last round is)
(this later became any variable number of rounds, but for now we'll assume that the game lasts at most 7 rounds).
Then if a game gets to a 7th round, you know that it's the last round. So if I take the copycat strategy and modify it to "copy what your opponent did in the previous round, unless this is the 7th round, in which case, cheat no matter what", then I will beat the copycat strategy in the long run. Similar for all of the modified strategies that sometimes cooperate. And then we can go further: once all of the strategies cheat in the 7th round, it becomes pointless to cooperate in the 6th round... and so on.
So I think that the game needs to be modified further to truly get the desired outcome. Maybe something like: "after each round, roll a 6-sided die, and if it's not a 6, play again".
