Shin Megami Tensei Persona [PSP Game]

The rumor around St. Hermelin High is that by playing the "Persona" game, you can get a glimpse of your future self. When the protagonist and his friends try it out on a lark, nothing seems to happen. But then the protagonist and his friends all share a common dream after blacking out, in which they meet a mysterious man calling himself "Philemon". Who and what could he be?