I'm not sure that would be less expensive overall than running a lot of DC current through wires strung across the arena — the Earth's magnetic field is approximately equivalent to that from a 250-amp current line at a distance of 1 meter, and (assuming you are inside the circuit, so the path of current going back the other way is not too near the first current) that falls off linearly. It also negates the neat thing of being about magnets — the insight that a compass operates by detecting some physical force which can be manipulated, rather than by orienting you absolutely in space. Come to think of it, doing it by GPS is exactly backwards!

Maybe a board game like Stratego, but where some units contain magnets (including current lines — it would be fairly simple to run a few volts between two layers of the board and have pieced bridge between them) and some units contain compasses?