It was fought from 2011-14.
(It's never come up in an actual game as yet, but I've always ignored the - very unchacteristically - badly thought-out retcon by Chris Hartford in
The BattleSpace Rulebook, that even poor Mike "Cray" Miller couldn't manage to further retcon into something believable in
Jihad: Terra, about the Warsaw Pact unraveling in 1984 and then being forcibly reconstituted in a Soviet Blitzkrieg in 1997. For my own purposes, I assume that most of the history of the Cold War was the same as in the real world until 1988, when Mikhail Gorbachev died in either a genuine accident or an assassination disguised as one, following which Glasnost and Perestroika were abandoned in favour of a reversion to the bad old ways for the next 17 years.)
Either way, economic collapse in 2005 brought another reformist leader named Oleg Tikonov to power, but he was assassinated by a jihadist suicide bomber in 2011. Then rival factions in the Communist Party and the military turned on each other in the Second Soviet Civil War. Eventually NATO invaded successfully in 2014 to end the anarchy and the 7 (not 15 as in the real world) successor polities subsequently spent decades under Western Alliance occupation. Oh, if only!
Edit:
Either way too, technology progressed a good deal faster, with military scramjet spaceplanes in the 1980s, a permanent modular space station in the 1990s, orbiting laser platforms capable of shooting down ICBMs by the 2010s and of course a working fusion reactor design in the 2020s. Again, oh, if only!