Not only does this solve the public goods problem, it suggests a new libertarian strategy: nuclear revolution.
This is from my response to _____ (that's seriously his name)-
Let's assume that you're a customer of a retaliation business, and terrorists get a hold of a nuke of their own, and try to use that to threaten people. Now the retaliatory agency has a choice-- mutual destruction (of customers and terrorists, that is, not necessarily the company itself), or give in to the terrorists. You'd think they'd give in to the terrorists.And in fact, the defensive strategy is the only ESS here. Because of this, the field is wide open for revolutionaries-- provided they stick to the defensive strategy. The governments of today, as far as I know, use no systematic nuclear strategies, and would have little credibility if they threatened to use a nuke offensively-- the risks wouldn't be worth the benefit.
But the people running these retaliatory agencies are probably going to be smarter than that (if they get any business). The game theorists behind MAD put a lot of emphasis on credibility, that is, the likelihood that the company will actually go through with mutual destruction if attacked.
In your thinking, the company didn't have any credibility, and thus the defense could be overcome. But an effective company is probably going to have some kind of mechanism in place that guarantees that any transgression will end in mutual destruction. If terrorists threaten customers, they are destroyed, guaranteed.
Maybe the source of a guarantee is a computer program that controls the nukes/whatever and can't be altered. Maybe the company agrees contractually to pay an outrageous sum if it doesn't follow through. There's room for experimentation here.
If the thread of MAD is credible, then a society using a defensive strategy can't be invaded by an agressive strategy. (I mean "invade" in the game-theoretic sense -- attackers always get a lower payoff than defenders. Attackers are guaranteed to die, while defenders have a good chance of coming out alive. The defensive strategy is an ESS.)
So if a defense company got a hold of a nuclear weapon, or contracted with someone else who had one, they could conceivably hold the entire world at bay. Their customers could live lives unhampered by organized coercion.
Freedom is only one nuke away.