So, moral of the story is: Reward good behaviour.
Being "nice" (copycat) is not the same as being a "sucker" (cooperator).
Suckers don't make things worse just for themselves, but for everyone around them, by encouraging bad behaviour.
Even then, people make mistakes, so don't hold grudges for too long. They won't lead you very far.
The problem I see only pops up when there are more interactions - when the player knows the other will cheat, but still decides to cooperate.
I wish. This is an oversimplification.
In many real-world scenarios bad behavior wins unless the rules of the game are changed to encourage cooperation.
E.g. by social norms or legislation or contract
The morality depends on where/who you were when the system/rules changed.
In those games, best move is to exit the room. Cause no reward/punishment system work.