How did the brinkmanship lead to an arms race between the us and the soviet union?

Jon F Kennedy sorry fro all the rush im going to class but yea

It was when President John F. Kennedy played brinksmanship with Soviet Premier Nikita Khruschev over offensive missile installations in Cuba. In the end, a compromise was made, which resulted in the removal of nuclear weapons in Cuba and United States' ally which is Turkey. The nuclear was prevented.