Competition for a game. Free entry, $10k prizepool, legal?

Hi guys,

We are thinking about promoting a competition to help launch our mobile game.
The prizepool will be ~$10,000 USD and it will be free to enter.
It will be available worldwide and the winner will be paid through PayPal.

The winners will be decided based on skill - how well they score in our game.
We will verify results through Apple's Game Center.

My question is:
[B]Is this legal and are there any fees/forms/certificates I need to attain to promote this competition?[/B]

Thanks!