The rental market analogue of a dark pool is the rental market. All transactions are secret by default, allowing higher-information parties (landlords) to set prices that are advantageous to them, and prevent transactions from moving the market.
These algorithmic pricing systems extend that information advantage by pooling information across landlords (maybe not illegal by itself) and leveraging their position as market-wide price-setter to push rents higher, with the promise that so many units are following their recommendations that renters have ~no alternative (very illegal price fixing)
The rental market is a decentralized network, with companies like these the network gets routed through a central node and the operator of that node has pefect visibility while the connections being routed have no idea what every other connection is doing like a dark pool, it's the centrality that makes it an analogue.
I could think of several advantageous moves like artificially inflating rents then favoring a well paying client by keeping their rents lower than the market. Investing in property spread out across shell companies and then have the algo favor them in a non-intuitive way.
Dark pools don't provide sellers or buyers an asymmetrical advantage[1] and prices are still set by participants and cleared at market, not set by the operator of the exchange (i.e. dark pool).
[1] if they're both participating in the pool, clearly an institution seeing pricing signal from an alternative trading system (even if it's only their own cleared trades) has more information than someone observing only public market transactions.
These algorithmic pricing systems extend that information advantage by pooling information across landlords (maybe not illegal by itself) and leveraging their position as market-wide price-setter to push rents higher, with the promise that so many units are following their recommendations that renters have ~no alternative (very illegal price fixing)