You might like "Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb" (https://www.amazon.com/Prisoners-Dilemma-Neumann-Theory-Puzz...)

It is not a secret that Von Neumann's work on Game Theory at RAND corporation in the 50's was precisely commissioned by the US government to answer the first strike question.

Here is a quote from Wikipedia: "In 1950, the first mathematical discussion of the prisoner's dilemma appeared, and an experiment was undertaken by notable mathematicians Merrill M. Flood and Melvin Dresher, as part of the RAND Corporation's investigations into game theory. RAND pursued the studies because of possible applications to global nuclear strategy."

https://en.wikipedia.org/wiki/Game_theory

And another on RAND corp: "Its most visible contribution may be the doctrine of nuclear deterrence by mutually assured destruction (MAD), developed under the guidance of then-Defense Secretary Robert McNamara and based upon their work with game theory."

https://en.wikipedia.org/wiki/RAND_Corporation

A great fun and entertaining book on the subject: https://www.amazon.com/Prisoners-Dilemma-William-Poundstone/...