Both! Often, market anarchists don’t find these philosophies, properly contextualized, to generally be at odds.
Classical liberals (a.k.a. market liberals) advocate a free market economy. Socialism seeks a world where the means of production are owned by workers. Many market anarchists believe that freed markets lead to that world. The state-granted monopoly privileges and rents deigned to the purchasers and wielders of political power removed, the amount of economic opportunity available to working class people would outpace the bureaucratic and artificial economies of the existing corporate-dominated marketplace.
We believe that market anarchism should please almost all people influenced by these two complementary traditions.