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When will we meet grabby aliens?

Robin Hanson, Daniel Martin, Calvin McCarter and Jonathan Paulson have a new paper out about grabby aliens. From the abstract,

According to a hard-steps model of advanced life timing, humans seem puzzlingly early. We offer an explanation: an early deadline is set by 'grabby' civilizations (GC), who expand rapidly, never die alone, change the appearance of the volumes they control, and who are not born within other GC volumes. If we might soon become grabby, then today is near a sample origin date of such a GC. A selection effect explains why we don't see them even though they probably control over a third of the universe now. Each parameter in our three parameter model can be estimated to within roughly a factor of four, allowing principled predictions of GC origins, spacing, appearance, and durations till we see or meet them.

Scott Aaronson wrote a qualitative summary of the paper here. Figure 8 in their paper provides a cumulative probability distribution for when our descendents will encounter grabby aliens, under various parameter settings in their model.

This question is important for long-termists, since it provides one constraint on the overall size and power our civilization will eventually have. Assuming that human descendants do not have the ability to conquer neighboring alien civilizations, our descedents will be constrained by the amount of resources we can "grab" in a phase of rapid expansion and colonization, much like the European imperialists of prior centuries.

In how many years will humanity's descendants meet grabby aliens?

This question resolves as the number of years since 2021 that human descendants (biological or artificial) physically encounter "grabby aliens", defined as aliens that consume at least 10^26 watts of power, corresponding to Carl Sagan's proposed definition of a Type II civilization on the Kardashev scale. For the purpose of this question, to physically encounter an alien civilization means that any part of their technology is within 1 light year of any part of our technology.

ETA 2021-02-22 In case humanity goes extinct before it meets grabby aliens, it resolves as ">10^16".

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