Simplest after 4...Ba6 is simply 5 axb5 Bxb5 6 Bxc4 ! White is clearly better and scores about 70% from this position. Its possible that 6 b3 ! is even better .
Odd response to QGA
I think I am looking at the game of Kasparov's to which you are referring to. His opponent is called "Comp Elite A/S" and the game is from 1985! It seems to be from a simul event in Hamburg, Germany where Kasparov faced a number of chess engines simultaneously. He scored 32/32!
I find Kasparov's continuation the most convincing.
So after 1. d4 d5 2. c4 dxc4 3. e3 b5 4. a4 Ba6 5. axb5 Bxb5 6. Nc3 c6 7. b3 with 8. bxc4 to follow white is, in my opinion, going to be better out of the opening.
While playing live chess today I came across this response to the QGA which I haven't seen before.
I've always learned that 3. ...b5 was a dubious move by Black, and so I happily played 4.a4 going for the usual traps (4. ...bxa4 5.Qxa4+ followed by 6.Q(or B)xc4 regaining the gambit pawn with lead in development and 4. ...c6 5.axb5 cxb5 6.Qf3 winning a minor piece). But my opponent played 4. ...Ba6 instead, and that caught me by surprise. The game continued quite evenly after that until I blundered away a rook, which kind of annoyed me since 3. ...b5 is supposed to be a mistake.
So, how should I capitalize on this response? I tried searching past databases but this seems to be a pretty rare occurence...there's a past game of Kasparov's where he responded 5.axb5 Bxb5 6.Nc3 c6 7.b3 e6 but the position seems quite even after that (although Kasparov won in the end anyway so I might have missed something. Or maybe he's just that good. XD) So is there any other response?