Markets can easily exist without government. Goods were initially bartered for, traded for other goods. Government currency standardizes the system of trade but money and currency needs not be issued by the government. There are a lot of people tired of the Governments interference and manipulation of money through central banking and the fiat system. CryptoCurrency is flourishing and will continue to do so as more people awaken to the fact government creates more problems than it solves.

A good read is What Has Government Done to Our Money? by Murray N. Rothbard