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 thought your post asked about the proposition "o=ASK => a=PAY", and didn't mention the other one at all. You asked this:

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

not this:

Do you precommit to pay?

So I just don't use the naked proposition "a=PAY" anywhere. In fact I don't even understand how to define its truth value for all agents, because it may so happen that the agent gets $1000 and walks away without being asked anything.

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.