According to Kojima, he began using the title by his own accord. While Kojima points out that recently it is being used by others, the reason why he uses it is because he plans the project, designs the game, pens the script, directs the game and overseas the project.
Of course, he has not added “A Hideo Kojima” game to Metal Gear Solid: Rising or the new Castlevania title he is producing. Those are not Hideo Kojima games.
Japanese websites have been quick to point out some of Kojima’s colleagues that have been also using similar title cards. Dead Rising 2 is a “A Keiji Inafune Game”. Inafune worked with DR2′s developer Blue Castle Games and produced the title.
Inafune produced the first Dead Rising but did not write or direct the project.