Usually, more competition means lower prices and higher quality as less effective businesses go out of business. However, it appears that it's not always the case. When there're a lot of health insurance companies, each of them has relatively little bargaining power with service providers (hospitals) and, as a result, prices are significantly higher compared to a hypothetical government-funded single-payer system. Is there any free-market solution? What libertarian scholars (they exist, don't they?) would suggest?
There's another example, social networks. Facebook was selling user private data without them realizing it but never went bankrupt or lost a lot of users. It's evident to me that it's due to its oligopolistic nature. You can't nationalize Facebook or do something similar to what is proposed for health care by American presidential candidates like Bernie Sanders. You also can't promote the creation of many new tiny Facebooks because the social network user wants to have all their friends, family members, colleagues, favorite celebrities, etc. available in one place so people would unwittingly gradually monopolize "the social network market" back by opting for the network with more users than its competitors.
Are there any studies that found any umbrella solutions (preferably, ones that don't involve socialism) for cases when simply promoting competition doesn't work?