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If interested in the subject, I'd recommend William Poundstone's Prisoner's Dilemma, which I've recently completed. This book contains three parts to it. They interweave in chronological order and are obviously closely related.
The first, is a colorful history of the interesting polymath John von Neumann was. It provides his personal background, professional history, and the circumstances surrounding his introduction of Game Theory.
The second portion is a broader history of Game Theory and particularly, in its relation to cold war era events and strategy at the time. The United States govt paid for the research leading to its advent and the intersection of science and the politics of the mid 20th century world is quite interesting. Much information regarding the nuclear project and related developments, the OP reviewer mentioned finding interesting, can be found here. Game Theory was in fact quite consequential. Discussion of other Game Theorists and debate and development of the subject can also be found.
Lastly, the book contains descriptions of Game Theory itself. Various scenarios, games, and the developments of each. This includes those mentioned above and more.
While the above is a brief synopsis, if looking to broaden knowledge of the field and have a more colorful read, I would explore Poundstone's title.