I just hate Arcade so much. But I will say this is one of the best uses of Joker in one of these. It's not so much a team as an escalation so that means Joker doesn't have to do anything with anyone, though I assume he'd have to buy into Arcade's plans or Arcade would kidnap him too and that'd be an issue itself.
The way I see it, Joker would buy into Arcade's game for the sheer fun of it and because he gets to be the final boss. I think it'd be right up his alley.