Now obviously you should be able to do even better than that. You should be able to take one another's estimates into account, share evidence, revise your estimates, reach a probability you both agree on

Hold on. I assume that, in accordance with a normal Prisoner's Dilemma, the two players aren't allowed to discuss stuff. So this is out.

Edit: And lo, MBlume added the following to his post:

I'm starting with them together, and free to speak briefly, for reasons which will be clear soon enough.

In that case, they can simply agree to take 10,000 of each. This is obvious.

Edit again: This seems inconsistent with my later view. Hmm.