Well, intuitions can sometimes be completely off. But of course, tit-for-tat is just a general strategy it doesn't mean that you have to apply it blindly, without e.g. tuning the parameters. And, as far as I can remember, there are slightly modified formalized versions, where you allow for the other party cheating/competing without immediate retortion.
The idea is, that of course, in real life people are not 100% uniform, miscommunication and misunderstanding happens, etc. And you'll want to tune your parameters to the situation at hand. E.g. if you have a long standing relationship with the other actor and they've always been cooperating then you may not want to compete/retort when you see then doing it for the first time. (OTOH, what I personally found important is that in a new relationship, you should be very strict about this. Even if not immediately compete, shoot a very directed and serious warning.)
The general idea is that you don't let the other party to take advantage of you in the long run , but you always allow for de-escalation and don't try to take advantage of them in the long run either. (You will get taken advantage of, of course, because you'll always start cooperating, so if every other actor/player is competing then you'll lose on average. But not by much. However, if there are just a few one who are willing to cooperate most of the time, then you'll win big time.)
