You can formalize UDT in a more standard game-theoretic setting, which allows many problems like Parfit’s Hitchhiker to be dealt with, if that is enough for what you’re interested in. However, the formalism assumes a lot about the world (such as the identity of the agent being a nonproblematic given, as Wei Dai mentions), so if you want to address questions of where that structure is coming from, you have to do something else.
You can formalize UDT in a more standard game-theoretic setting, which allows many problems like Parfit’s Hitchhiker to be dealt with, if that is enough for what you’re interested in. However, the formalism assumes a lot about the world (such as the identity of the agent being a nonproblematic given, as Wei Dai mentions), so if you want to address questions of where that structure is coming from, you have to do something else.