You know, it’d be easy to recommend Fog of Love in this scenario except for the competitive streak. You can definitely game the game, try to “get good” and perform, but I don’t suspect really anyone would want to play it like that.
What it has got, however, is a very subtle mix of mechanics and deduction elements, with light roleplay*, that all flows like hot butter. The game has a tutorial from heaven, and it’s a game that should click with a wide range of personalities. You “compete” independently, but with an eye on your shared destiny as a semi-cooperative endgame.
Again, the biggest disadvantage is that it would likely be unpleasant if things are taken too competitively, but it’s got a ton of things going for it as a gateway game. Second disadvantage would be shelf-life, I suppose, but I share a differing opinion on that to most and it’s not something to get into here. Anyway, worth a look online to see what it’s all about.
*Roleplay in this case can be as clinical as making choices that suit the goals on your card (there are synergies galore in this game BTW), all the way out to let’s-LARP-this-badboy.