Bluetooth response time

Bluetooth response time

I'm want to making a game that would involve N number of android phones
connected by bluetooth.
The game is suppose to be a reactor game (like the one you can find on
android market, but I want to make it playable on multiple phones), so it
is important for me to know who pressed the button first and my question
is: is it possible to do it with bluetooth?
I planed it to be like this: user1 will open the game and open a "new
game" and all of the other user would open the game in their phone and
join this "new game" and when everyone has joined user1 would start the
game. Every time someone presses the button (you know how this game
works...) a signal would be sent to the main phone (to user1), but when it
is sent there is a delay before the main phone gets it and when user1
clicks there is no delay because it doesn't have to send the signal. How
would I eliminate this difference?
I actually don't have any experience with bluetooth and only little
experience with android programing, so if there is someone who has some
free time to help me you can see my email address on my profile.
Thanks