Economically speaking, which system of health care would be most efficient? Single payer, free market or other?

[yep]

I am aware that there is often a discrepancy between social efficiency and competitive efficiency, and sometimes markets may only achieve the latter and create deadweight loss. I also know it is true that monopolies (like single-payer) often create DWL also, but can be efficient in some cases, maybe where there is induced demand involved.