Medal of Honor: Vanguard for PS2 does not have a co-op or multiplayer mode.
The game is solely focused on a single-player campaign, putting you in the shoes of a paratrooper fighting in World War II.
While there are other Medal of Honor games for PS2 that feature multiplayer modes, like Medal of Honor: Frontline and Medal of Honor: Rising Sun, Vanguard is strictly a single-player experience.