My boyfriend been flirting with another girl on fb , should i play the same " game " back ?

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My boyfriend and i have been together for 4 months. He gave his password to his fb 2 weeks after we stared dating . I couldn't help but to snoop another , as i signed he got a message of a girl saying she'll date him . I couldn't help but do read their messages .. She was saying his cute and that she will date him . i went through his other messages once when he barely had 2 months together and every time a girl will flirt with him , he will tell them that he has a girlfriend , you know to back off . But with this girl he exactly send " OH MY GAWD , YOU'RE SO PRETTY /-\ <3 " . My boyfriend loves soccer ( and well i really hate sports , the only thing i do is use a skateboard ) and he thinks girls who play soccer is a huge turn on and he always wanted a soccer relationship . Oh guess what ? She's in the girl's school soccer team just like him , and when he found out she made the team he got happy because they might go to tournaments together . Okay after the girl said he will date him , he asked her to kik ( messaging app ) him . Now i'm worried hes just flirting with her through kik so i wont see . He also checks out other girls in school and acts like an ass with his friend . ( he made fun of me because i self-harmed while we were dating ) but he said he stopped . He was also holding hands with his girl best friend to supposedly get her boyfriend jealous . He gets sort of jealous when im with my guy friend . So i mean why cant i play the same " game " back ? Every time he does some stupid crap ' i always end up apologizing or forgiving him . I wanna show him that i'm not always gonna go running back to him . I know its kinda childish and i should just talk to him but I wanna show him he actually has game , you know? My main questions are :
- how can i show him he has game but not push to far to breakup ? or
- He is just cheating on me ?
- what should i do ?