Russia claims to have inherited that capability from the Soviet union, but that claim looks increasingly suspicious, with the war in Ukraine exposing not only systemic corruption in the Russian military, but also near-total failure on the intelligence front: officials were lining their pockets with funds destined to maintain and enhance military capabilities, and Russian generals were greeted with precision strikes upon arrival in Ukraine. If they can't keep their sh*t secret from Ukraine, how could they hope to keep a nuclear launch order secret from the US? A nuclear arsenal also requires expensive upkeep to remain functional, money that might also have been used to buy fancy appartments and yachts in London, Cyprus,... At this point it's questionable whether Russia would even be able to launch a succesful first strike and not see it intercepted by the US (they might still be able to land more than zero succesful strikes, but taking out US strike capabilities is a wholly different ball game).
Of course it's possible that other players might rise to be a threat, but basically I'm saying we should first check how realistic the scenario is before analyzing the whole situation through the lens of those overly simplified game theory models.