Bryan Caplan and Edward Stringham expand in Networks, Law, and the Paradox of Cooperation (PDF) on Caplan's critique of the thesis by Tyler Cowen and Dan Sutter that the anarcho-capitalist ideal of private defense firms is impossible due to the structure that industry would form.#

Cowen and Sutter (1999) argue that libertarian doubts about the viability of collusion are inconsistent. How, they ask, can free-market economists be simultaneously optimistic about the private production of public goods, but skeptical about collusion? Collusion is, after all, a public good vis-a-vis competing firms. Cowen and Sutter's challenge may be dubbed the Paradox of Cooperation: Laissez-faire can cope with either the monopoly or the public good problem, but not both.1 Libertarians who dismiss concerns about collusion are at best over-confident.

Cowen (1992) goes further by claiming that in so-called network industries, libertarians are not just over-confident, but wrong: Laissez-faire leads to monopoly, not competition. Although his network industry argument poses a challenge for more moderate libertarians too, Cowen primarily employs it to expose the fundamental weakness of the radical anarcho-capitalist position (Rothbard 1978, Friedman 1989): An excellent example of a network industry is the very free market in defense services that anarcho-capitalists favor. In consequence, anarcho-capitalists are sorely mistaken about the consequences of their ideas if tried.

The paper very much follows the structure of the previously mentioned critique, but is expanded with references and detail.#

The authors bring up the issue of cooperations that are "self-enforcing":#

Cowen here conflates two radically different sorts of business cooperation under the generic heading of "collusion." Standardizing products is essentially a coordination game, fixing prices a prisoners' dilemma. As long as consumers want a uniform product, adhering to industry standards is self-enforcing. As long as consumers prefer to pay less rather than more, price-fixing is not. Ability to reach the cooperative outcome in the former in no way "implies" ability to reach it in the latter.5

The authors also mentions an important point about how to measure the success, or failure, of a collaboration and identify that is possible to have partial success in such endeavours:#

First consider the effectiveness of partial participation. Voluntary collaboration never yields unanimity. But howinjurious is the shortfall? This hinges on the elasticity of outsiders' behavior. Suppose that 50% of all firms in an industry join a cartel to restrict production. They will be unable to raise prices much because outsiders' supply curves will typically be elastic. Firms that refuse to join the cartel increase their output to exploit the situation. Indeed, if outsiders' supply is perfectly elastic, strict unanimity is crucial; any departure from 100% participation renders the cartel impotent. In contrast, if 50% of all people who benefit from clean air decide to "do their part" by buying low-pollution cars, they can make a significant dent in the problem. As long as the outsiders already pollute to the selfishly optimal point, an improvement in the level of air quality has no effect on their marginal incentive to pollute. Half of the drivers pollute less; half pollute the same; air quality improves. Of course, neither the cartel nor the clean air movement fully solves its public good problem. The point is that voluntary pollution abatement is a partial success, whereas the voluntary cartel is a full failure.