Founded on April 1st, 1998, by Tim Cain, Leonard Boyarsky and Jason Anderson, three men made famous for their work on a certain post-nuclear roleplaying franchise.
The company only developed three games (barring a pitch for a third Fallout game) before closing their doors on February 24th, 2005.
Fun fact: "Troika" (Тройка) is a Russian word meaning "three of a kind", chosen as a reference to its founders.