During the Cold War, the USA and Russia engaged in an arms race against each other and started developing nuclear weapons. Some mathematicians have said that logically it is better to use nuclear weapons than to not use them. But some mathematicians said it is better not to use nuclear weapons.
Because the mathematicians did not agree among themselves, Albert William Tucker, game theorist, invented “The prisoner dilemma.” Imagine you rob a bank with another guy, and you are being interrogated about the case. You are A and the other guy is B. A and B know, if A says it was B and B says nothing, B must be in prison for 5 years and A is free and vice versa. If A says it was B and B says it was A, they both must be in prison for 10 years. If they both say nothing, both must be sentenced to 1 year in prison. If you are just seeing it from your point of view, it is better to tell the other person, but if you are thinking for you both, it is better not to say anything.
And that´s the reason no one began a nuclear war. One can relate the trapped dilemma to other situations in life as well, for example if you are in a group. It is a bit like a mathematical proof for “One for all and all for one.” There are also the iterated prisoner's dilemmas. That is when the prisoner dilemma happens with many people several times. In this case after many rounds the copying prisoners are the majority.