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swestrup comments on Counterfactual Mugging - Less Wrong
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When to believe what claims is a completely separate issue. We are looking at a thought experiment to get a better idea about what kinds of considerations should be taken into account in general, not to build a particular agent that does well in this situation (and possibly worse in others).
Is the scenario really isomorphic to any sort of real life dilemma though? An agent which commits to paying out the $100 could end up being screwed over by an anti-Omega, which would pay out $10,000 only to a person who wouldn't give Omega the $100. I'm not clear on what sort of general principles the thought experiment is supposed to illustrate.
Start from assuming that the agent justifiably knows that the thought experiment is set up as it's described.
Do they know before being confronted by Omega, or only once confronted?
If they did not know in advance that it's more likely for Omega to appear and conduct the counterfactual mugging than it is for anti-Omega to appear and reward those who wouldn't cooperate on the counterfactual mugging, then I can't see that there's any point in time where the agent should expect greater utility by committing to cooperate on the counterfactual mugging. If they do know in advance, then it's better to precommit.
It's an assumption of the thought experiment that the player justifiably learns about the situation after the coin is tossed, that they are dealing with Omega and not "anti-Omega" and somehow learn that to be the case.
In that case, it doesn't seem like there's any point in time where a decision to cooperate should have a positive expected utility.