According to the About Market Anarchism page of the web site of the Molinari Institute, a market anarchist or free-market anarchist 1) think tank:
“Market Anarchism is the doctrine that the legislative, adjudicative, and protective functions unjustly and inefficiently monopolised by the coercive State should be entirely turned over to the voluntary, consensual forces of market society… The terms 'anarcho-capitalism' and 'voluntary socialism' have both been associated with the Market Anarchist tradition.”
Variations of market anarchism include agorism, so called ”anarcho-capitalism”, mutualism, geoism, voluntaryism and others.
Market anarchism overlaps with the term ”left libertarian” with three notable exceptions:
1. Those who prefer the term “anarcho-capitalism” often exhibit a tendency to downplay or deny their ideological common ground with advocates of anti-state socialism, often to the point of conceiving of themselves as “right wing” or “right anarchists” and exhibiting what are generally regarded as right-wing cultural attitudes. It should be noted that this is at odds with Rothbard's placing of libertarianism on the far left of the political spectrum opposite statist conservatism, with state socialism as a confused centrism (the pursuit of liberal ends through statist conservative means).
2. Some self-described left libertarians are not anarchists and instead advocate a mix of minarchist and social democratic (“liberal”) views.
3. Some avowed anarchists also describe themselves as “left libertarians” (as opposed to market oriented “right libertarians” in their view) but are hostile to the insights provided by the market anarchist tradition because they equate a market economy with capitalism or corporatism.
The genre market anarchism has two distinct branches.2) One branch, called propertarian market anarchism, recognizes all economically scarce goods as legitimate property.3) This includes “natural capital” such as land, but does not necessarily include non-scarce goods such as intellectual property (patents, copyrights, and trademarks). Propertarian forms of market anarchism include agorism, anarcho-capitalism and voluntaryism.
The other branch of market anarchism, called non-propertarian market anarchism, treats property titles on land as illegitimate, not exchangeable within the free market.4) Non-propertarian forms of market anarchism include geolibertarianism and mutualism.5) Unlike the propertarian forms of market anarchism, mutualists support a possession or “occupancy and use” basis for land. As for capital, mutualist opinions differs on whether these should be commonly managed assets or private property.