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Honorable mention: we haven't detected alien probes, because intelligent alien societies haven't begun consuming the galaxy with exponential numbers of self-replicating robotic probes, because that's just a really bad idea:
Oh my god, that's such a stupid and simple way to kill a galaxy, but also what a great plot twist that would make in a story. Like the big reveal over why the galaxy has always been at war with itself. Exactly the kind of nihilism I'd expect from an Altered Carbon or its ilk.
Thanks for sharing!
You might like the paperclip maximizer thought experiment
Also an excellent clicker style game called Universal Paperclips
Thanks I have heard of this kind of problem before, just not in an adversarial space war context, with like opposing forces
There's an easier and more reliable way to limit replication; don't hive them the means to create a small but essential part, and instead load the first probe woth many copies of it and have each replica take a set percentage.
For instance, have the probe able to replicate everything but its CPU, and just load up a rack of them on probe 0. Every time it replicates itself it passes half of its remaining stock to the replica and they both carry on from there.