To solve this, Samuel Konkin proposed a market solution (agora = market). In a long polemic, he claimed that by working on the black market, libertarians could spur a gradual economic secession from the state. More and more people decide to work on the black market, until the state either gives up or loses all relevance.
Like their legal counterparts, black market entrepreneurs respond to incentives. Thus, black market activity can be modeled economically.
A black market entrepreneur avoids taxation and regulation, and this acts as a subsidy for his business, relative to his legal counterparts. He also pays extra to escape government harassment, and this acts as a tax.
The main determinant of the existence of a black market is the relative sizes of the subsidy and the tax. If the subsidy is greater than the tax, the good is provided cheaper on the black market, and the black market thrives. If the reverse, it's provided legally.
Konkin isn't very clear about why he expects agorism to succeed, but the 28 years since the publication of his essay have not been kind to his thesis. Black markets have only been widespread for goods that have been outlawed — marijuana, illegal immigrant labor, and so on. (In cases where a good is banned, its legal price is infinity— it can't be bought legally— and this guarantees it will be sold on the black market, if at all.)
Later I will discuss network effects, more problems with agorism, possible solutions, and the potential of this strategy.