In the Fallout games bottle cap are used as currency. As crazy as that sounds it actually works and there is benefits. First of all there is a limited number and while a manufacturing plant or two did survive the war, it's tightly controlled by a merchant group.(more on that in the next paragraph) Since a crap ton of caps existed before the war then there is no reason to create new ones. If anything this group prevents inflation by not creating new caps. One cap = 1 US dollar and in the game a 10 mm pistol(a gun that existed before the war) in Fallout 4 can be bought for under 100 caps. Now compare that the US dollar cost of the real life equivalent.
The second is that caps cannot be counterfeited. I meant what I said about that merchant group. I think it's in New Vegas where a group of criminals discovered a bottling plant that had machinery that worked in terms of creating bottle caps and they started to flood the market with these caps. You can do a quest where you put the group and the machinery permanently out of business.