I believe the field of research your referring to is called Peer-to-Peer Information Retrieval. Doing a search on it will bring up many papers published on it g

I believe the field of research your referring to is called Peer-to-Peer Information Retrieval. Doing a search on it will bring up many papers published on it going through the various attempts, issues with and theories on building such a system that's sufficiently good enough to be competitive with a centralized search engine.