This should only matter to the extent that the agents have to act simultaneously or near-simultaneously. Otherwise, whoever goes second maximized utility conditioned on the choices of the first, and so on, so it’s no worse than if a single person sought the local maximum for their giving.
Of course, the difference between local and global maxima is important, but that has nothing to do with the OP, and everything to do with TDT.
This should only matter to the extent that the agents have to act simultaneously or near-simultaneously. Otherwise, whoever goes second maximized utility conditioned on the choices of the first, and so on, so it’s no worse than if a single person sought the local maximum for their giving.
Of course, the difference between local and global maxima is important, but that has nothing to do with the OP, and everything to do with TDT.