It might end up looking like a random "employee of the month". There are thousands of individuals working on their own little puzzle piece of these large cooperations, singling out some individual contributors "down in the trenches" for an award would be a lot more disrespectful to their peers than awarding some shared head figures who implicitly represent their entire extended teams.
I was thinking that the prizes would go to smaller individual discoveries, rather than to the major ground breaking discoveries. I.e. either the prize would be basically for theoretical physics, in which case Higgs could get the prize (and no one involved in confirming it would be awarded). This would basically leave experimental physics out of the question because these huge experiments obviously always involve huge amounts of people.
Or the awards would go to small discoveries that actually were made by individuals or small teams. Basically you'd see the largest and most groundbreaking discoveries go completely unawarded because they are group efforts, and since the price is directed towards the lone genius, it would be awarded for tiny discoveries.
But are there even small discoveries in physics? Anything not predicted by current models would be considered huge, and everything else would not be a discovery.