TDT is underspecified. Vladimir Nesov claims that you can set it up by hand to pay, but others are skeptical.
Yes, I believe that the consensus is that counterfactual mugging is considered a pretty good argument, if you had to choose between TDT and UDT. But it would be nicer if there were a formalization that indicated what class of problems they agree on and what (larger) class UDT is right. Without such a formalization (and maybe even with one), TDT provides a different perspective and one should not discard it. Also, it is possible that there is an example where TDT beats UDT.
I didn't see a direct answer to my question there, but he did write
TDT considers the current possible world, as explicitly depending on agent's decisions. As a result, any site where agent's decision influences the current possible world, in the past of in the future, generates a collection of counterfactual worlds that TDT agent also takes into account. In particular, on Newcomb's problem, agent's decision is located in the past, and opens both possibilities for consideration. In Newcomb's with transparent boxes, the agent should update on the state of the second box and exclude the possibility of its alternative state, but because its decision site is still located in the past, this decision site allows to regenerate the alternative with the different state of the second box, and so TDT agent acts correctly on transparent Newcomb's.
So maybe TDT can regenerate the alternative where the coin landed heads and Omega is considering whether to pay you the $10000.
I'd prefer a simple yes/no, though.
TDT was defined as "deciding in such a way as if it decides the outcome of the abstract computation that is its choice", which I assume means doing so in such a way to maximize expected utility. If TDT pays, its past self has expected utility of $4950, while its current self has expected utility of -$100. If TDT doesn't pay, its past and present selves both have expected utility of $0. It sure would be counterintuitive if TDT didn't pay, and time stopped a timeless decision theory agent from winning/being consistent.
On one hand, this old article said TDT doesn't pay. On the other hand, I imagine TDT not paying would be a slam-dunk argument for favoring UDT, which pays, and I haven't seen people make that argument. So I'm confused here. Thanks.
Edit: this wiki page explains all the jargon