I'm playing The Elder Scrolls: Tamriel Unlimited and there we have local auction houses. (Thy don't have auctions, but I keep the term to not get confused in the following text.)
I can see the advantage that guilds (who own these AHs) can set up their own little economy, which is a nice feature.
On the other side I always have to check several guild traders to see which one offers my searched item for the lowest price.
On the forums, people are discussing heavily whether a global auction house should be introduced or not. This may have pros and cons, too, but I'm not too involved in this game design to really set up a mind for that.
Backers argument that an global AH leads to a more regulated market, easier to use and a seller will reach a broader audience (reads: When you put in an item, you can be sure that there may be a buyer.)
On the other hand critics say that this will make only really useful items get a massive increased price and common used items will drop their prices to their normal selling price.
But are these concerns really true? Would the introduction of a global AH really have such a big impact on the game's economy? And if yes, will they more tend to even the prices or really make most of the items useless for selling?
You could also ask vice-versa: If a game already has global AH, what would the impact be if they replaced it with local auction houses?
What is the difference for the game's and players' economy if you introduce a global or local auction house system?
For clarification: I do ask this for the matter of The Elder Scrolls: Tamriel Unlimited. But you can also subject this to other games. (This should be more a theoretical question for a developer's decision.)