Sounds like what you'd want for a self-hosted Dropbox clone. I wonder what Syncthing, for instance, uses for reconciling differences on different clients.
Syncthing does recognize conflicts. When a file has been modified on two devices simultaneously, one of the files will be renamed to <filename>.sync- conflict-<date>-<time>.<ext>. The device which has the larger value of the first 63 bits for his device ID will have his file marked as the conflicting file. Note that we only create sync-conflict files when the actual content differs.