1) Consists of both private companies and government/state owned entities. For example, UIC and IIT in IL, USA. The former is a public college and the latter is a private college.
2) Both have control of owning, making, selling and exchanging goods in the country and thus have equal control over the market. For example, in USA the GDP contribution of the public and private sector is nearly equal.
3) Government can control some parts, but not all. For example, the USA government controls the police, fire department,etc.
4) Monopolies can occur but the government closely monitors this. For example the Sherman Antitrust Act, a federal law passed in 1890 that committed the American government to opposing monopolies. The law prohibits contracts, combinations, or conspiracies in the restraint of trade or commerce.
5) Government rules and regulations, which have to be followed by private businesses. The federal minimum wage is one good example.