I don't care who I trade with. No one does. It's anonymous anyway, unless you trade with certain official market makers. Also, I don't care if my one order for 400 shares@$100 matches with 1 person selling 400 shares@$100 or 400 people selling 1 share@$100.
Trade matching is not the stable marriage problem. Get a clue.
You certainly care what the price on the other side is if you are getting the spread or some fraction of it. That is what determines the preference ordering to run the algorithm.
Trade matching is not the stable marriage problem. Get a clue.