In truth, you can probably get to wherever you want with any related or similar degree. Degree's can open doors, but experience is king.

If you want to do programming then a software engineering or computer science degree is probably good. You could also get these sorts of jobs with a maths/physics degree (if you can demonstrate/learn a programming language in your spare time).

Alternatively, if you're dead-set on games producer/programmer and will accept nothing else then look at the specialist courses in game development/design.

As an aside, I was told by the HR people were I work now that the broader subjects are better in the long-run. I have a computer science degree - I can get into game development with that, and I can also get a regular software engineering job (like I currently have). I'd of found it a bit difficult to get my current job if I had a "Games Development" degree... it's silly, but the people who employ in these labs probably still look down on a games degree ("Are you serious?", "What use is a games degree for real business?").

Your profile says you're currently in the UAE - I don't know how things work over there, so don't really have any specific advice. As for "hedio kojima", I don't know who he is and a google search for a profile/history of him didn't yield anything.

hth
Jack