Earlier quoted context omitted.
Free market means free from monopolies as well.
Nonsense. Free market means the ideal market of whatever one's personal ideology thinks will work best. It's the economic version of "a perfect world", and everyone has a different vision of what "a perfect world" even means .
Free market, which btw has grown to become a economical and political buzzword, is not "the ideal market of whatever one's personal ideology thinks will work best"; The core ideology behind it was to let the buyer and seller work on what works for them and keep third party interference to the least.
Fair market imply either party is made aware of all the details behind the trade in case of which price discovery is impossible as the buyers won't buy above real value and sellers won't sell below real value. Anti-trust and Anti-monopoly laws that are sub-points of a fair market are inherently against the ideal free market.
Also, theory does not really work in practice and no market is entirely free or fair.