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:

Omega problems do not (normally) require Omega to be assumed a perfect predictor, just a sufficiently good one.

Well, fine, but then the correct strategy depends on Omega's success rate (and the payoffs). If the reward given to those willing to pay is r, and Omega's demand is d, and Omega's prediction success rate is s, the expected payoff for those who agree to pay is s r + (s - 1) d, which may be both positive or negative. (Refusers trivially get 0.)