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The Railroad, being a clandestine organization, wouldn't want to draw attention to their agents (or to expend limited resources) attempting to manage a separate currency, though I could see them engaging in counterfeiting, if they could find a way. Caps work, and no need to deviate from that. However, given the scarcity of both (and yet the potential for an explosively HUGE find to turn up), it would be neither practical nor stable in an economy the size of the Commonwealth. The Minutemen, if truly inspired by the US Constitution, might wish to re-establish a system of exchange based on Gold and Silver coin. I could see there being an exchange rate for caps, even within the insular and isolated Institute, which would need currency for its infiltrators to use within the Commonwealth. Regarding the Institute having its own currency system, that should have been a given. I don't see the BoS having much reason to trouble themselves establishing a separate economy, since they trade all across the continent, and having a ready-made economic system simplifies their own mission, while their explorations would net them substantial financial resources in caps they collected or looted from fallen enemies. However, once a vault has been exposed to trade with the outside world, pre-war money would stabilize at the value it has in the Commonwealth, where it can be found in substantial quantities, but is more commonly used as a crafting resource. Vault-Tec clearly allowed for the potential post-war use of pre-war money, given its prevalence within vaults after the war.