The PlayStation 2 console cannot play games made for the PlayStation 3. It is capable of playing games designed for the PlayStation 2 and original PlayStation consoles only.
The PlayStation 2 disc drive reads DVD and CD formats. The PlayStation 3 disc drive reads Blu-ray, DVD and CD formats. Because PlayStation 3 games are in the Blu-ray format, and the PS2 console only reads DVD and CD formats, it does not house the necessary technologies.
While the PS2 cannot play PS3 games, some early models of the PlayStation 3 console are capable of playing PlayStation 2 and PlayStation games. These models have been discontinued.