Extremely Counterfactual Mugging or: the gist of Transparent Newcomb

Bongo

Omega will either award you $1000 or ask you to pay him $100. He will award you $1000 if he predicts you would pay him if he asked. He will ask you to pay him $100 if he predicts you wouldn't pay him if he asked.

Omega asks you to pay him $100. Do you pay?

This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.

Here's a diagram:

Omega will either award you $1000 or ask you to pay him $100. He will award you $1000 if he predicts you would pay him if he asked. He will ask you to pay him $100 if he predicts you wouldn't pay him if he asked.

Omega asks you to pay him $100. Do you pay?

This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.

Here's a diagram:

Could you explain the error, rather than just say that it is a common error? How can I agree to pay in a situation which happens only if I was predicted to disagree?

(I don't object to having precommited to agree to pay if Omega makes his request; that would indeed be a correct decision. But then, of course, Omega doesn't appear. The given formulation

Omega asks you to pay him $100. Do you pay?

implies that Omega really appears, which logically excludes the variant of paying. Maybe it is only a matter of formulation.)