Develop an app/game

I am looking for someone to develop an app for me. A game for groups to play on their iphones (and others if possible).
Aimed at teenagers/students. It will involve them all joining a simple game individually. Then going through a few rounds until one player emerges the winner.

I'd like it to look nice, clean and modern but there won't be a need for any complex animation. Mostly static imagery. But maybe a few of them spinning or moving. Perhaps making the phone vibrate at times to build tension.

I have no idea how much these things cost or how long they take, so I put £600 down as a first stab.
I will need you to give me some idea of the cost and we would need to agree a figure for final delivery before we start working together.