Free-market anarchism or market anarchism includes several branches of anarchism that advocates an economic system based on voluntary market interactions without the involvement of the state.
A branch of market anarchism is left-wing market anarchism such as mutualists or Gary Chartier and Kevin Carson, who consider themselves anti-capitalists and self identify as part of the socialist movement.
On the other hand, people who identify as anarcho-capitalists stress the legitimacy and priority of private property, describing it as an integral component of individual rights and a free market economy. There is a strong current within anarchism which does not consider that anarcho-capitalism can be considered a part of the anarchist movement because anarchism has historically been an anti-capitalist movement and for definitional reasons which see anarchism incompatible with capitalist forms.
The term may be used to refer to diverse economic and political concepts, such as those proposed by anarchist libertarian socialists like Pierre-Joseph Proudhon and Benjamin Tucker or alternatively anarcho-capitalists like Murray Rothbard and David D. Friedman.
Mutualism began in 18th-century English and French labour movements before taking an anarchist form associated with Pierre-Joseph Proudhon in France and others in the United States. Proudhon proposed spontaneous order, whereby organisation emerges without central authority, a "positive anarchy" where order arises when everybody does "what he wishes and only what he wishes" and where "business transactions alone produce the social order." It is important to recognize that Proudhon distinguished between ideal political possibilities and practical governance. For this reason, much in contrast to some of his theoretical statements concerning ultimate spontaneous self-governance, Proudhon was heavily involved in French parliamentary politics and allied himself not with Anarchist but Socialist factions of workers movements and, in addition to advocating state-protected charters for worker-owned cooperatives, promoted certain nationalization schemes during his life of public service.