I know that the only winning move is not to play, but put yourself into the shoes of Dr Strangelove or Herman Kahn. What are the best games in the style?
Balance of Power is a classic, but there you need to avoid a nuclear confrontation.
DEFCON has cute graphics, but is obviously not a WarGames-style simulated Global Thermonuclear War.
Bravo Romeo Delta is getting interesting, but what is happening behind the curtain?
It does not have to be a commercial video game or necessarily a computer game at all; maybe there was a real version of the military wargame depicted in the movie? Someone somewhere was and is contemplating the unthinkable; they have to learn somehow.
The problem with DEFCON is that there is no way to avoid nuclear war - your opponent (the computer) escalates the situation to an all-out nuclear exchange regardless of whether you want it or not. That was the biggest irk for me in what was otherwise a pretty good budgetware game.