A Zigbee module might work, but it depends on exactly how large the space is as well. I hope you got cash, if you found someone to make them as cheap as possible you're looking at 5 dollars for a zigbee module, 5 dollars for a battery and 2-4 dollars for everything else (I'm just guestimating) So figure 15 dollars per bracelet that's 15,000 dollars for 1,000 people.
There are other methods that might work as all you're doing is trying to sync all of the bracelets, a simple micro controller and an ultrasonic receiver could be made much cheaper, probably in the 2-5 dollar range, a single large transmitter, or a network of smaller ones (much more practical) would send out a sync signal, as this is powering LED's line of site is assumed and a local oscillator could be used to keep time in the short term if the sync signal is lost.