But Bezgodov's results are not really impressive; according to my database, he has played 2.a3 four times, scoring 2.5 points, but against weaker opponents, so he actually lost rating points (his average is 2550, his TRP with 2.a3 is 2515).
Vladimir Dobrov scored somehow better: 8.5 points from 14 games, also against weaker opponents, but he reached a TRP of 2517, his own mean rating being 2503.
With almost all second moves, Black scores more than 50 %, the only exception being 2...Nc6?!, where White scores 58 %, and the quite rare 2...a6?!. The point after 2...Nc6?! seems to be 3.b4!?, when White gets a (probably) reasonable version of the Wing Gambit, scoring 62%, but that might be due to his much better knowledge of the "theory".
Richard Palliser (in Fighting the Anti-Sicilians, Everyman 2007, p. 239 ff) recommends 2...g6!, which is indeed both the most common and statistically one of the most successful moves (from Black's point of view, White scores only 40 %); a secondary line is 2...e6 (also quite common and scoring well for Black), after which White doesn't seem to have a good answer.
There is also quite some coverage here in the Anti-Sicilians section with 12 annotated games; I hope I don't violate too many copyright laws when I quote one comment form Andrew Martin at the beginning of the latest game covered (Klings-Bruno, Capo d'Orso op 2008):
Quote:The individualistic nature of 2 a3 cannot be disputed, but I have often wondered what happens when Black just ignores b2-b4 and carries on developing. We have seen frequently that 2 ...g6 is a good move; now consider another perfectly decent reply for Black [which is 2...e6 - Zzz].
(By the way, White lost that game.)
Best regards,
Zwischenzugzwang