Read in Judith Merril’s The Year’s Greatest Science Fiction and Fantasy, 1956.
Reprinted in Asimov’s ‘Earth is Room Enough’ collection, so I will have read this in about 1974, as I diligently collected all of Asimov’s books and read them cover to cover in my early teens.
Asimov posits a new technology, ‘dreamies’, a form of immersive VR, but instead of being digitally coded, the dreamies are created by capturing and editing the dreams of the small percentage of the population who dream vivid dreams. Rather than creating a longer narrative story, the story is set in the office of Jessie Weill, owner/founder of Dreams Inc., whose busy afternoon sees a number of visitors, through which Weill/Asimov can ponder various implications of the technology – the impact on those whose dreams are captured, the creation of pornographic dreamies, and whether (as per the title) people will want to enter into a shared experience, or keep their dreams private.
In terms of forecasting the tech, top marks for Asimov for people disappearing into other worlds, but he didn’t quite get the porno element right, nor the rise of MMORPGs.