According to Idiom Quest (IQ), "Two can play that game" means — You retaliate against someone in the same manner that they hurt you. Unfortunately, it seems that acting out this idiom occurs all too often in relationships. Some women are emphatic in stating; "If he cheats on me I'll cheat on him" and have done it. The hurt does not necessarily have to be emotional as there are other mind games that people play. If a man repeatedly does not answer his phone when a woman calls then she may also not answer when he calls. If a man goes out every Friday night, some women start going out every Friday night as well. These tit for tat scenarios are indicators that your relationship is probably not healthy.
There are interesting perspectives on people who live by this idiom. One such perspective is that they were simply waiting for an opportunity. In other words, they are opportunists. Could it be that those who retaliate in like manner when hurt in a relationship subconsciously wanted to do exactly that 'thing' they did all along? I am not sure and I won't judge anyone but I am aware of victims who derived great satisfaction from playing those games as well.
Sometimes it is not necessary to play the same game; it is best to play the 'I have let you go and you don't know' game. Here, the victim, tired of the games, pretends they don't know what's going on when in fact they are fully aware of all the lies and the mind games of the other person. Unbeknownst to the game player the victim has moved on. The victim initiates fewer contacts with the game player who eventually gets the picture, hopefully.
Relationships should not be about games but sadly some people play them and worse, it's all some people know. Everyone handles these games differently as I have pointed out. Two can play that game but in playing that game with the other person what does it say about you? Does it mean you are a tough person who can dish it out as good as or even better than it was dished out to you? Does it mean you are a vengeful person? Does it mean they got you to compromise your standards and morals and become a different person?
Look at it this way, if they cheated and you cheated in return who won? Would you have cheated if he didn't? Most likely not, which means he made you stoop to his level, unless it was something you wanted to do. Sure two can play that game but do you have to play the same game? "He made me do it, he turned me into this" is a familiar cry I've heard from victims. How about rather than waste time playing his game you move on? Emotional pain and turmoil can be awful and one can experience a range of emotions, not all being rational. However, let us not forget that life is about choices; choosing to play a game because someone played it on you is your choice. Two can play that game but you don't have to play it too, particularly if it means changing who you are.