Yes and no.
The economy is largely reliant on players and the many crafting trees (which require some real dedication), mostly due to the rarity and versitality of gold. Gold in ESO is very rare to come by, mostly obtained by selling useless items or broken down components. Gold is used in everything from purchasing items from vendors, to fast travelling to wayshrines when in the middle of nowhere, to upgrading and improving your gear. So naturally, you want to get as much as you can.
The crafting is extremely in depth, and dedicated players can spec their skillpoints into greatly improving their craft. For instance, a master armorer could create epic-level armor for level 50 players and sell it for a good bit of gold. Not only is this possible but it's all but neccessary to do this stuff for the best gear, weapons and potions. In that essence, the economy is highly player driven. Crafting is also much, much cheaper than purchasing the gear but again that requires a good bit of dedication if you want to craft everything you use.
However, from what i understand, the game lacks an auction house; the pinnacle of P2P trading. You can set up your own little shops but have no way to really get the word out there (i am basing this from what I knew at launch and from my time playing the beta. They might have added an auction house since then but I can't confirm).
So yes, it's player driven, however it's not easy to trade globally. There are guild stores that act as mini auction houses, but are only available for members of the guild. This isn't necessarily a bad thing though, and the economy is still mostly reliant on what player craft and are able to find.
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Thanks for the in depth reply. I'd love an auction house but Defiance didn't have one so I made a forum shop. So I guess I'll go that route. Again, thanks.
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There are actually several 3rd party auction houses online. Good websites already made to compensate for the lack of it in-game.