I haven't worked out the details but intuitively it seems like it should.  It seems a lot like counterfactual mugging.

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If you mean reparations in the modern political sense of, eg, paying members of ethnic groups that were mistreated by past generations, then decision theory is mostly irrelevant because the arguments in favor of doing that come from a completely different angle.

In FDT, the argument for paying back past harms is a selfish one: if you're the sort of person who will predictably pay to repair the damage if you harm someone, people will be more willing to associate and trade with you. Whereas the modern political argument for reparations is an altruistic one: we like fairness and people flourishing, so when there's a legible group that is not-flourishing for reasons that are unfair, we want to change that.

There isn't any sort of general principle that would lead to paying reparations in all or even most circumstances, no. Reparations do make sense in the context of specific social structures and incentives. For example, an agent that can demonstrate that it will likely pay reparations if appropriate in the future may be able to make better trades with other agents in the present.

However, multi-agent coordination is unsolved. Reparations are just one fragment of a potentially infinite set of coordination protocols, and nobody has mapped out all possible such protocols.

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This seems like it would be a real tough call, as the rules by which such things are decided change over the course of the period under consideration.