The forum isn't big enough to do this. Nor could it ever be officiated adequately.
Already enough trouble is involved with trying to organise games, and once those games get played, teams are still disputing and arguing over it
True GTA players shouldn't need a cash prize to motivate them to play any way.
I've suggested to Rockstar Mouth Off
a few times, to organise stuff themselves, they usually do a lot of "Play with Rockstar" events, but never actual competetive modes for the hardcore gamers to battle it out. It seems like they might be heading in that direction though, with the expansion of multiplayer in Max Payne 3 and the increasing amount of Rockstar Social Club interaction with multiplayer, as seen with RDR and now with this upcoming concept of "crews".
Maybe R* themselves will host cash prize competitions.