re: .

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Though without any regulation, monopolies are almost certain in the long run

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Not necessarily. The main things that helped to create monopolies of the late 19th century were government privilige and protection (and it should also be noted that by the time the anti-trust act went into effect, Standard Oil had already been losing on the market).

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Change the said competitive judicial system to a monopolistic non comp. one.

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Well, then you have arrived at our current arrangement.

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Furthermore say in the short run where there is competition, multiple privatized police firms and prison systems could potentially be disasterous. Whose going to arrest the CEO of iPoPo? Does he not have his own army?

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Unless an individual is habitually violent and found to be a genuine threat to society, I very much doubt that prisons, or arrests for that matter, would be very common. They are not economically viable when one relies on customers' patronage to pay the bills. I think ancap justice would be more restitutive than simple imprisonment.