I feel the other answers make too many assumptions outside the scope provided. I think that shared has these pro and con considerations.
Furthermore, I think the restocking option should be revisited on the purpose no matter what option is chosen. Restocking, unless for more realistic impact on the game world, doesn't make any sense if there is a delay. I think a reason on why there is a restock should be clarified more in the underlying mechanics.
Shared
Pros
- More realistic system that could be attractable to players.
- Ability to lock the market, where you can buy everything and resell for higher.
- Ability to prevent others from buying certain items such as a warfare tactic.
Cons
- Players can troll other players by buying everything in the shop until it's restocked.
- Players could get frustrated in the buying process if they are to slow to purchase before someone else snags the item.
- Restocking times can conflict with players play times, especially in diverse time zones.
Private
Pros
- Potentially unlimited and exclusive supply could devalue immersion to the player.
- No one person controlling the entire market.
- No one person denying you access to items in the shop.
Cons
- Could devalue immersion for those who want more realism in the shop system.
- Limited ability to lock the entire market and resell for higher.
- No ability to deny others access to items in the shop
Explanations
Locking Down The Market
EVE Online is a player driven economy. Buying low and selling high is a trader tactic that is common in the game. Regardless of who you are buying from, NPC or not, the tactic is very attractable to players.
Likewise, buying all items or useful items from a station is considered a warefare trade tactic. This is to prevent your enemies from getting much needed supplies to fight you or escape. Like the previous example, this is a tactic that is very attractable to players regardless if the seller is an NPC or not.
I feel that this being a negative is entirely subjective.
Market Control
Having control of the market may be attractable for players who want to trade. Although it may be bad for the economy, a bad economy may be a good scenario for the game. I know that sounds bad, but trading in most games is widely popular. Simulating trade, both good and bad trade can be good for the gameplay experience.
For example, a game that include both bubbles and when they burst. Surviving a great depression and more could be both rewarding and challenging for traders, while also destroying the economy. The act of destroying and repairing could be fun for players.
More Realistic
Buying out items and restocking can be looked at as being realistic or a sign of realism in the game. Some players really enjoy these types of designs. Restocking for one good example could include a trade merchant that physically arrives at the shop and restocks it. This opens up additional gameplay experiences for players who may want to hijack the shipment before it even arrives. Likewise, players who want to protect it.