I don't believe government is necessary at all.
Anything currently handled by government institutions can be handled better by the free market, including security and arbitration, even punishment if we manage a shift in mass opinion from expecting government to punish those who need punished to realizing it need to be done by the community directly. For example, a private arbitration service could determine that someone is guilty of murder. Instead of expecting a government entity to handle this, the community should execute him directly.