The Game Designer's Group isn't a company in and of itself, but a loose collection of authors and designers from other game companies who come together for... well, it mush be for something, but none of the members are clear on exactly what, other than that dues are $80 a year.
Once every spring the Group holds an Industry convention (called GDG) at a randomly-selected location in a far-flung corner of the US, where for three torturous days writers beg for work, Industry employees pat each other on the back, and company representatives bore retailers in trying to shill their latest products.
Background Information Edit
The Game Designer's Group is likely a parody of Game Designers' Workshop. Unlike the GDG, GDW was a separate company, and collapsed in 1996, four years before Subsidiaries was published.