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:

I don't even understand how to define its truth value for all agents

Seems to me that for all agents there is a fact of the matter about whether they would pay if asked. Even for agents that never in fact are asked.

So I do interpret a=PAY as "would pay". But maybe there are other legitimate interpretations.

If both the agent and Omega are deterministic programs, and the agent is never in fact asked, that fact may be converted into a statement about natural numbers. So what you just said is equivalent to this:

Seems to me that for all agents there is a fact of the matter about whether they would pay if 1 were equal to 2.

I don't know, this looks shady.