That doesn't make any sense. There is a dramatic under-supply of housing, there will be no "out-competing". They're going to rent all of their apartments, the price-fixers and the non-price-fixers. They'd just be leaving money on the table, not "out-competing". They're not going to magically acquire a bunch of new non-existent housing to grow their market share. I implore you to move beyond econ 101 thinking.