There's no game theory involved. A million years is a blink of an eye on an evolutionary timescale. When the first civilization has Von Neumann machines, their closest competitor is most likely primordial goo. See http://andabien.com/html/evolution-timeline.htm to get an idea of how long it takes for life to evolve.
Even if there were multiple civilizations in a galaxy, a single "defector" civilization would have vastly more matter under its control than civilizations that did not use Von Neumann probes to expand. With such a huge advantage, they would quickly destroy all competitors.
No, but then I don't understand the imperial incentive, even here on Earth. I'm a fairly self-centered individual, and a lazy one at that... and as far as I can see, running an empire always seems to be more trouble than it's worth. The whole history of the twentieth century can be written in terms of the world's great powers discovering this little tidbit of truth. I believe the first few decades of the twenty-first will see the US experiencing the same global comedown that Russia, Germany, and Britain have already undergone.
Fortunately, the loss of its empire is a process that always seems to leave the nation in question better off, at least in modern times. As I see it the only possible justification for total galactic conquest is self-defense: do unto others before they can do unto you, more or less as you put it. Any advanced civilization that doesn't see that as a self-defeating justification is so different from my way of thinking that I couldn't possibly deal with them on any terms, offensive or otherwise.
Basically, what you're saying is that the only way to survive and prosper in the Universe is to be a murderous, psychopathic douchebag on a galactic scale. Not down with that, sorry.
The fact that the solar system has sat around for 4 billion years without being eaten by Von Neumann machines makes me pretty certain that we're alone
Were these your words, or not?
You're projecting human flaws and attributes on an advanced race that would, by necessity, be almost nothing like humans. It simply does not follow that because the solar system has not (yet) been turned into grey goo, we must be alone in the galaxy.
So this hypothetical civilization has conquered aging, death, and the drive for rapid gratification, but fails at elementary game theory?