I live in Bristol and for a certain commodity N (the number of players) is vastly greater than one, yet without argument it is agreed a truly unfair monopoly exists.
And if you're British I have no doubt you too are experiencing this.
Water, the stuff that comes out of your taps and is also sold in bottles from very many suppliers.
Basically the number of players in a market isn't the best indicator of how competitive that market is, but rather what share of the market does the main player have.
In the case of water, the local supplier has a natural advantage, and has no problem in pitching its price to dissuade all but the heavily marketed bottled water pushers. So. many players fighting over a fraction of one percent of the market, while one player controls over 99% of the market.
In China's case, the price it charges for the low hanging fruit that is lanthanum and cerium need only be low enough to hurt its competitors. It can charge what the hell it likes for the higher grade elements knowing full well no other producer could match that price and satisfy total demand.
And let's not forget, we live in a world where the market plays with us. China's economy is such that it can chose to play with the market as it wishes.