Here below a table showing the possible relationship between property rights and type of economy from the preparatory works of one of my future works)
Planned vs. market economy
Gianluca di Castri (IdeaConsult)
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Gianluca di Castri (IdeaConsult) 
I wonder if it is not also (and perhaps above all) the role of a sovereign state (for example its role as regulator and consequent direct intervention in the economy) that determines a structure of the free or socialist economy.
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In my opinion a sovereign state should manage its economy and then decide whether its market has to be free totally or partially, etc. The globalization, that brought a lot of positive effects, has given too much power to the finance over the economy. While big bankers have been a strong power also in the past (Fugger, Medici, etc,) the state had an higher power that could impose limits to the power of finance (I know, sometimes with methods that are not allowed any more)
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