Once gold loses its value, players often turn to other currency that they use for P2P trading (like the classic Stone of POE Items Jordan in Diablo II).GGG solved most of these problems by canceling gold all together. POE has no currency that is used only for trading - every single item in the game has some intrinsic functionality and value. Thus, there are many items that are considered "currency items" in POE - each does something different when consumed (providing a natural money sink mechanism):

Let's say I find a good item while progressing in the game, but I don't need it at the moment (perhaps it doesn't fit my current character or maybe I already have a better one). Often I would try to "sell" it - list it publicly hoping to trade it to another player in return for some currency. The idea is that, like in any true free market, the item might not hold value for me - but does hold value for someone else, so we can make both of us better off via an exchange (assuming he gives something of value for me in return).
In principal I could try trading it for a different piece of equipment that I do need (instead of some currency items) but, just like in the real world, this type of barter has numerous disadvantages and is almost never used.

As in most RPGs, in order to trade the two players must be in the same game zone. This seemingly trivial requirement actually creates a natural friction in the trading process. Usually while I'm in the game I'm, well, playing the game - so when a potential buyer sends me a message that he is interested in something I have for sale, I must stop what I'm doing and go meet the buyer at some location (one of POE Currency the towns or player "hideouts"). The process usually takes less than a minute if both players are used to trading in POE, but it's somewhat annoying and partially breaks the game flow.