It's not that simple at all. Several times systems and procedures were set up to trigger nuclear escalation, and even though those sytems and procedures indicating making an attack, the person who had the final say in doing so chose not to. Thsy didn't make that choice necessarily knowing about game theory or Nash equilibriums, they weren't following deliberately concieved national strategic policy. They just made a judgement call.
You don't need to know anything about game theory to say "hey, I don't want to start a nuclear war and think I should precede very cautiously."
The only two incidents I'm aware of where it got that close, one was stopped by an officer before it even got up the chain of command. The other got to Yeltsin, who made the very rational call to wait and see if there was an error before starting a nuclear war.
