Take, for example, the problem of limiting CO2 output. This is a global problem; there is no way to realistically privatize it. but, at least the people under the same treaty could tax the common forms of CO2 output.
Charging per ton of CO2 output, many economists believe, is better than simply regulating how much CO2 a person can output because by giving it a dollar per tonne value, you are encouraging the market to eliminate CO2 output where it's cheapest and easiest to do so, while allowing the market to continue to output CO2 where it would be really expensive to avoid.
'cap and trade' is a variation on this that is similar but different; instead of setting the economic price of a tonne of carbon, for example, you set an absolute limit for how much carbon can be released, and then lets the market decide what to use that for.