You should do something akin to "Capture the flag"
1) Allow the players to select playing area (in sq feet)
2) Allow players to designate teams (assign each GPS device 'red' or 'blue')
3) Split playing field in 1/2 (1 for red, 1 for blue)
4) Further subdivide the player grid into small blocks (lets say 25 on each side), and allow the player to decide which grid-square they will hide their 'flag'
5) When the game starts, normal CTF rules will be enforced, except the flag is digital, and in order to 'capture' they must enter the correct "square" of the opponent, and then return to the correct "Square" in their home base. If tagged, the flag is "Dropped" in the current square. To register a tag, determine if two opposing players are in the same "square".
For this to work, there will have to be enough "grid squares" so that a team cannot simply block an entire row or column.