That's quite different from the hypothetical earlier, because you're now describing multiple owners rather than a single monopoly. If a single corporation owns

That's quite different from the hypothetical earlier, because you're now describing multiple owners rather than a single monopoly. If a single corporation owns all homes, they can artificially limit supply by buying up any new properties and leaving them empty. If multiple companies own all homes, then they can try to artificially limit supply by buying up any new properties and leaving them empty, but there's huge incentive for each one not to: if it rents out every property it buys, it makes even more money than if it left any of them empty. It's the prisoner's dilemma - if all companies collude and limit supply they maximize total profit, but if any individual company "cheats" it stands to gain even more for itself. It is possible for cartels to collude and pull this off (OPEC etc), but it's not possible when there are thousands and thousands of companies and many of them are too small to "take one for the team" and leave a property empty, or too disinterested in any collusion.