I've been playing Path of Exile and I wanted to give some feedback on that game not having an Auction House.
The game has an API for public stash space. There you place a price per item (or per tab, I assume). This allows the API to cache it on the website. You open the website (or 3rd party site) and search for the item you want.
On the one hand it's pretty neat that you are still required to PM someone (oddly enough there's a PM button that will copy a predefined message for the seller) but the problem is when someone is AFK or uses an item to 'price fix'. For items this isn't an issue however for currency it's a huge problem.
PoE doesn't have gold as a currency, it has 100 types of currency. The same API that is used to sell items is also used to sell currency. One big complaint from players is people are using bots (although not against ToS for PoE trading of currency) so they don't need to be at that screen for trades. The next complaint is people will price fix (as mentioned above) so that certain currency pairs look cheaper than they are. The next complaint is a request for the PoE developers to add a currency AH (or Exchange) so that the trading can be done without bots or people needing to be online and not afk. But really people not wanting to trade is a thing.
I know people want to chat with others to trade but the reality is that many people want to play the game while trades happen. We have the carpenter, so I'll suggest a Barker (or Broker) that can sit at someone's house or at a trade district in a town/city. This allows the player to list items, and they get to play the game. When they come home they can check to see which items are sold. This system was in Dark Ages of Camelot back when and it was pretty neat, annoying at times but still pretty neat. The Barker/Broker API can be used so we can access it in game or out of game.
The Barker/Broker is a currency sink too!
This still makes people run into the world (at least the Barkers not in a city) for goods to be traded.