In fact, it would be great fun, and worth doing intellectually, to run
a game-theoretic simulation of this problem. Could get an Icarus
publication out of it. Any worthy coauthors interested? :-)
Let me try to sketch out the strategic situation here.
A new civilization like ours knows that a shell of our early radio
signals is expanding out at the speed of light, and that this may
trigger "berserker" probes flying in at near the speed of light to
destroy our solar system. So some folks may want to get the hell out
of here and try to colonize elsewhere. They'd want to go as fast as
possible, to escape a possible detonation wave of unknown size and
speed (could someone nova our star, or galactic center?), or a
followup wave of berserkers. And they'd also want to not send signals
back to Earth that such enemies might intercept - signals would have
to look like cosmic background to someone without the right key (and
with the home base keeping your location info very localized, on a
hair trigger to destroy it.) They'd also want turn a corner
somewhere, so their path away from Earth (ionized regions) doesn't
lead right to them. And not knowning how far they might be followed,
they'd want to go a good long way.
New colonies might try to hide themselves better, but even then some
of the locals may get itchy of being traced, or growing too big not to
be seen, and try to escape. Within any system, keeping the quiet is a
public good, so a strong central policing might be required to enforce
it.
Star systems might also consider lying low until their technological
advancement seems to asymptote, and suddenly "running for it". Grow
the local economy as fast as possible, not worrying much about being
loud, to support a massive explosion of colonization probes. They
might get 10^10 to 10^20 probes out of the system off to all corners
of the universe before enemies arrive. Or considering the costs and
risks of strong central policing, they might decide to just run for it
from the very beginning.
A civilization may also want to try to "test the waters", by sending
one probe to a distant system to try this "running for it" strategy,
and to then watch the results. They might also try a "loud mouth"
strategy in such a distant system, broadcasting as loud as they can to
see who responds how. Of course just how far away is "distant" is a
tricky question.
The strategic situation of a potential berserker is also complicated.
If they see a sign of a new civilization, and they send a probe to
destroy it, it might be a trap which lets someone else find them and
destroy them. If there are many other civilizations around, why
should they be the one to spend the resources and take the risk to
destroy the newcomer? And if they wait a bit, and still no one else
destroys it, that may just be because others have send probes to sit
near this new site, waiting for catch incoming destroyers.
If you want to send a probe to not only destroy this system, but to
infiltrate it enough to find out if it is a colony of some other
system, and where that system is, you will have to have your probe
slow down more, and more risk being caught by enemies who might trace
it back to you, especially if you were going to forward that info back
to your home.
It seems to me that the outcome of all this strategizing is that the
best strategy is just to expand as aggressively as possible. By the
time anyone comes to destroy any one system you have used it well,
converting it to a billion probes or much more within a few years.
That huge economy gives you all the better chance to learn new
technology, so some of your descendants become as advanced as your
advanced enemies.
To verify this intuition, an explicit simulation would be appropriate.
Robin D. Hanson hanson@hss.caltech.edu http://hss.caltech.edu/~hanson/