I was thinking of buying Playstation 3 for my sone. Since different brands can be played on the Wii, is the same true with playstation 3? Can playstation 2 games be played on playstation 3?

My friend bought a used Playstation 2 game and it won’t work in her playstation 2 but yet it works in mine.
All other games work in hers just not this one game….
Why is that?

Can I play playstation 1 games on playstation 2???