The article presents a mathematical model of a multi-stage game of the process of safe control of a transport object in possible collision situations with other encountered objects, containing a description of state variables, state and control constraints, and sets of permissible object strategies. Multi-criteria optimization tasks were formulated in the form of positional and matrix games under the conditions of playing non-cooperative and cooperative control as well as non-game optimal control. The multi-criteria control algorithms corresponding to these tasks were computer simulated in Matlab / Simulink on the example of a real situation.