Police have determined that GABRIEL AUBRY was responsible for his fight with OLIVIER MARTINEZ in front of HALLE BERRY'S house on Thanksgiving Day. According to their version of the events, Aubry shoved Martinez and then took a swing at him . . . which only managed to land on his shoulder. Of course, Martinez answered with three quick shots to the face, which ended the fight. And although police are concerned with Aubry's ongoing anger issues, both Halle and Olivier have said they don't want him prosecuted, because it wouldn't be in the best interest of Halle and Aubry's daughter.