One problem is that, in order to actually get specific about utility functions, the AI would have to simulate another AI that is simulating it - that's like trying to put a manhole cover through its own manhole by putting it a box first.

If we assume that the computation problems are solved, a toy model involving robots laying different colors of tile might be interesting to consider. In fact there's probably a post in there. The effects will be different sizes for different classes of utility functions over tiles. In the case of infinity robots with cosmopolitan utility functions, you do get an interesting sort of agreement though.