Nintendo, seemingly aware of the perils of interpersonal interaction online, have filed a patent for a "Massively Single-Playing Online Game," which aims to provide all of the benefits of a persistant online world, without any of the drawbacks associated with other people. The general idea is that a player's actions will affect various gameplay mechanics for all other players, much like in traditional MMOs, however the players will never actually interact with each other. A player may build themselves a house in a persistant world, for instance, and while other players can find the house, they cannot find its creator.
The Big N also gave economic examples, wherein a player's actions may increase or decrease the scarcity/value of an item for all players across the board. NPC interaction was also pointed to as a way for players to communicate with each other indirectly, with computer-controlled characters acting as messengers.
It's important to remember that technology companies like Nintendo file patent applications on a fairly regular basis, and that this application's existence doesn't necessarily mean that we'll be seeing this kind of gameplay implemented into anything anytime soon. It's also important to remember that a Pokemon game using this technology would be off the chain.