You need to plug your computer into one of them, and the PS2 into the other. However, I don't know if it's possible to get an adapter to connect a PS2 to either regular VGA or DVI.

I'm just about ready to take the plunge, and buy a PS2. I'd like to connect it up to my computer monitor (21" NEC MultiSync 6FGp), because we only have one TV in the house, and I don't want to ...

Now a team has taken on and managed the shocking task of porting Jak and Daxter, Naughty Dog's PS2-era action game, to a form that works on the PC.