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Are we assuming they are both equally skilled?
They will likely find each other to be rather elusive adversaries, and eventually the task will spiral out of your control. Professional pride will motivate each of them to 'catch-out' the other, and you won't even have to pay them anymore.
Maybe they will each hire an associate to help them out, so you will then have 2 pairs of investigators following each other. Even better, you hire two other investigators and instruct each of them to follow each of the other 3...
Pandemonium!
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