People in the nuclear post-apocalyptic world use bottle caps as barter money.
I love the series, so I can definitely answer with enthusiasm!
How would inflation work in such an economic environment?
In a fiat-monetary system, the supply of cash circulating in the system is defined and controlled by a central bank. Although the amount may seem arbitrary, i.e.let us print 100 million tomorrow, this would be extremely inflationary and as a result devalue the currency and its use within the economy. See Zimbabwe Dollar
But with bottle caps, the amount is fixed, but to a certain extent. Bottle caps can still be made. But as with all counterfeiting operations, newly minted caps =/= the consistency of old caps. The type of metal, paint, and even evidence of bottling may be distinctive enough to discern authentic caps from counterfeited caps. Nevertheless, the premise of the quest is that the trading company doesn't wish for the supply of caps to increase relative to demand, thereby retain the value of each cap in the long run.
In addition, metal caps wear out through use just like regular money. Although not represented in the game, this fact would act as a mechanism of which caps that have sufficiently deteriorated are removed from the system, acting as a deflationary mechanism.
How can people buy expensive objects like houses or maybe vehicles,
(they cost at least 10000)?
Take a look at the table of items and their assigned values. Given that markets will reach an equilibrium in terms of price for each item bartered, the cost of a rare or expensive item would be determined by those who produce the item and desire the item. Although one might argue that current theories of the value of labor may apply in a post-apocalyptic world, I don't think there would be a high need for economists in that dystopian future, despite the dismal setting.
But as for how, there will be a need for banks for wealthy individuals to store their caps given the weight and bulk of caps. At established settlements, it would be a simple matter for me to write out a contract to you stipulating and instructing the bank to transfer my caps to your name.
How would a bank know if another has launched a new version of purple
coin that is worth more than any other single bottle cap?
At least in lore, there are a handful of caps widely recognized by all factions: Nuka-Cola caps, Sunset Sarsaparilla Caps, and Bawls. At the same time, there are secondary currency systems: New California Republic Dollars, Legion currency, and Pre-War Money. All of which have (or had) a central authority, but not widely circulated or accepted. NCR money is not accepted in the Legion and vice versa. Pre-War Money has value, but isn't the primary means of currency use.
Given that all caps are equal, meaning no denominations, a user (regardless of status as a bank) would see if the logo on the caps would match his or her experience of caps that would be accepted by other participants in the market.
If a new bottle cap of unique color appears, how to corroborate that a
bank in another village supports its value? (that is, that is not
Over time, and given that there is no significant production anymore, there will be a set amount of produced bottles and their corresponding caps. Just like there are authenticity experts today to verify the origins of cars the same can be said for a new cache of bottles found. The drinks are opened and an article is published by the media that either supports or refutes the authenticity of the new cache.