When you interact with somebody else and you have to decide whether to cooperate with them or cheat them, the difference between the choices can sometimes be expressed in simple cost/benefit analyses. If we are generous with each other we might both reap the rewards. But maybe cheating is cheaper - unless you punish me for it. The mathematical analysis of these choices is called game theory.
When the cost of making the wrong choice is exceptionally high - such as in the case of nuclear standoffs - it is prudent to weigh the different options very carefully and hope that your opponent follows predictably similar logic. This is why game theory was widely applied in the context of the cold war.
In this review, Gil and Rutger explore four movies on this topic. A Beautiful Mind (2001) depicts the life and times of John Nash, one of the pioneers of game theory. Dr. Strangelove (1964) and Fail Safe (2000), based on the same book and basic plot, take nuclear retaliation to its horrifying logical extreme. WarGames (1983) shows that sometimes it is best not to play this game at all.
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