The AI gets positive utility from having been created, and that is the whole of its utility function. It's given a sandbox full of decision-theoretic problems to play with, and is put in a box (i.e. it can't meaningfully influence the outside world until it has superhuman intelligence). Design it in such a way that it's initially biased toward action rather than inaction if it anticipates equal utility from both.
Unless the AI develops some sort of non-causal decision theory, it has no reason to do anything. If it develops TDT, it will try to act in accordance with what it judges to be the wishes of its creators, following You're In Newcomb's Box logic--it will try to be the sort of thing its creators wished to create.
I'm having a hard time coming up with a motivation system that could lead such an AI to developing an acausal decision theory without relying on some goal-like structure that would end up being externally indistinguishable from terms in a utility function. If we stuck a robot with mechanical engineering tools in a room full of scrap parts and gave it an urge to commit novel actions but no utilitarian guidelines for what actions are desirable, I don't think I'd expect it to produce a working nuclear reactor in a reasonable amount of time simply for having nothing better to do.
At the recent London meet-up someone (I'm afraid I can't remember who) suggested that one might be able to solve the Friendly AI problem by building an AI whose concerns are limited to some small geographical area, and which doesn't give two hoots about what happens outside that area. Cipergoth pointed out that this would probably result in the AI converting the rest of the universe into a factory to make its small area more awesome. In the process, he mentioned that you can make a "fun game" out of figuring out ways in which proposed utility functions for Friendly AIs can go horribly wrong. I propose that we play.
Here's the game: reply to this post with proposed utility functions, stated as formally or, at least, as accurately as you can manage; follow-up comments explain why a super-human intelligence built with that particular utility function would do things that turn out to be hideously undesirable.
There are three reasons I suggest playing this game. In descending order of importance, they are: