I don't know if this is considered as a minigame or not, but I have a suggestion:
Why not make everyone tell AT LEAST one positive thing about the person? Like if you don't know them, just say that they're gorgeous or something?
I think it'd would boost somebody's self esteem and maybe even make a friend or two? :3
Or say two traits about yourself and see if anybody says that they are (almost or a lot) like those people??
Idk, just a couple ideas.