The market economy is a special kind of economy in which the economic decisions and ultimately the market is guided by self-interests and the prices. There is little, if any government intervention or planning involved in the process. Somewhere, the competition does influence the economy and serves as an invisible hand, which guides it as well.
However, the government and the corporations have minimal role in setting this economy. In addition, the central planners or the president doesn’t influence it either. It is purely based on individual interest and the consecutive prices.