Julia Bowman (1919-1985) was a prestigious American mathematician. She was the first female member of the Mathematics Division of the United States National Academy of Sciences, and the first female president of the American Mathematical Society.

She dedicated part of her scientific work to game theory, which is a branch of mathematics with applications in very different disciplines (sociology, psychology, economics, business management, military strategy, biology, artificial intelligence, etc.) that analyses the interactions between individuals who make decisions. In fact, Julia managed to prove a convergence theorem that is considered the most important one in Elementary Game Theory.

The following classic game is proposed: "The prisoner's dilemma".

The prisoner's dilemma is a fundamental problem in game theory. It analyses the incentives that two people suspected of a crime have to inform on their partner or proclaim their innocence. It shows how two people cannot cooperate even if it is against the interest of both.

The police arrest two people suspected of jointly committing a crime A and B. There is not enough evidence to convict them and, having separated them, each of them is offered the same treatment on a visit. If A confesses and B does not, B will receive the full sentence, ten years, and A will be released. If A is silent and B confesses, A will receive that 10-year sentence and B will go free. If both people confess, they will each be sentenced to five years. If they both deny it, all they can do is lock them up for six months for a minor charge.

This information can be summarized as follows:

Play several times with one of the students and try to find out which is the most convenient option.