Laser tag uses IR receivers and LEDs to simulate the actual shooting, right? So what if I made a system which uses a 200mw or so laser instead of an LED? Would this mean that I have to "hit" the receiver with the laser to trigger it? Or would it sense the light without that?
Also, how would I make actual vests when the IR receivers are only 5mm wide? Could I just use some sort of light dispersion technique?
It's fine with the right safety precautions. Glasses will be handed out to each competitor regardless of how strong the laser is. @LarryD mentioned that 50mw would be plenty, so I'll go with that if it's adequate.
It's plenty to cause permanent injury to the cornea.
Try something like 0.5mW in the green-red spectrum or <0.1mW for blue to UVA.
Your 'extensive project research' SHOULD have told you this already and SHOULD have alerted you that in your application only laser class 1 can be considered safe enough to even consider.
It's also irresponsible, unethical and exposes you to legal repercussions - rightfully so.