How I interpreted the problem- it's not that identical agents have different utility functions, it's just that different things happen to them. In reality, what's behind the door is behind the door, while in the simulation rewards X* with something else. X* is only unaware of whether or not he's in a simulation before he presses the button- obviously once he actually receives the utility he can tell the difference. Although the fact that nobody else has stated this makes me unsure. OP, can you clarify a little bit more?