The chapter considers the issues of mathematical description and formalization of autonomous intelligent machines functioning in economic systems. A definition of intelligent machines in the cyber economy is given. It is shown that intelligent machines could be effectively used to solve various economic tasks. We employ the tools of finite-state machines and game theory to describe intelligent machines in the cyber economy and illustrate the importance of machine learning and the methods of AI. It is determined that the best AI method is conformation learning that fully corresponds to the architecture of intelligent machines in the cyber economy. The authors show the importance of the creation of unified standards for describing the interfaces of intelligent machines. © Springer Nature Switzerland AG 2019.