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The prisoner's dilemma (revised table)

By Steven Schwartz - posted Tuesday, 1 November 2022

The district attorney has a problem. She knows that Mike and Clyde committed a bank robbery, but the evidence is insufficient to convict them. The suspects have vowed to remain silent to avoid betraying one another. To get them to change their minds, the district attorney separates them and makes each the same offer:

If you and your partner refuse to talk, you will each receive a one-year prison sentence on a lesser charge. If you agree to testify against your partner, you will go free, while your partner will get five years. If you both agree to testify against one another, you will each serve three years in prison

The following table summarises the options available to Mike and Clyde:


Option Mike's sentence Clyde's sentence

Mike and Clyde remain silent 1 year 1 year Mike is silent but Clyde testifies 5 years 0 years Mike testifies, but Clyde is silent 0 years 5 years Mike & Clyde both testify 3 years 3 years

As the chart shows, Mike and Clyde will minimise the time they collectively spend in prison (one year each) by cooperating and refusing to turn against one another. But the district attorney knows the temptation to get away with no jail time is difficult to resist. She believes the suspects will renege on their agreement to keep silent and end up behind bars for three years each.

Social scientists call the choice facing Mike and Clyde the Prisoner's Dilemma. It is a social "game" researchers use to understand how people make choices. Trial runs of the Prisoner's Dilemma confirm the district attorney's intuition. After weighing loyalty against betrayal, players usually opt for the latter. The result is a less-than-optimal outcome for both players. To an outside observer, betrayal appears self-defeating, but it is entirely rational from a participant's vantage point.

Consider the dilemma through Mike's eyes. He knows Clyde has two choices-stay silent or break his vow and testify. If Clyde remains silent, Mike should testify because he would then go free. If Clyde testifies against him, Mike should also testify because three years in prison is better than five. In other words, Mike's best move is to testify against Clyde no matter what Clyde does. Clyde, being just as rational as Mike, reaches the same conclusion. The result is that both robbers renege and wind up in prison for three years. This poor outcome is the essence of the Prisoner's Dilemma; people choose to renege even though their joint payoff would be higher by cooperating.


Betraying another's trust for personal gain is not exactly rare. Sellers who renege on contracts, athletes who take performance-enhancing drugs, and nations that send armies to attack their neighbours all seek competitive advantage but usually wind up producing a poorer outcome than could have been achieved by cooperation. The Covid-19 pandemic presents numerous examples. Masks, social distancing, hand washing, and vaccinations reduce the risk of infection. But masks are uncomfortable, hand washing is time-consuming, and social distancing means no hugs-so why not let others make the necessary sacrifices? Of course, if everyone adopts this attitude, the result is a higher level of infection for everyone.

Note, however, that there is a vital difference between the situation facing Mike and Clyde and everyday social interactions. The bank robbers are motivated to testify against one another because they never expect to meet one another again. They may be less likely to betray those with whom they have an ongoing relationship. Clyde, for example, may have made a different choice about testifying if the other prisoner was his lover, Bonnie.

In an ongoing relationship, is it always better to cooperate? To answer this question, Robert Axelrod, a professor of political science, organised a Prisoner's Dilemma tournament. He invited academics, students, and interested others to develop strategies for repeated Prisoner's Dilemma encounters. Each strategy was coded in the form of a computer program. A computer pitted the strategies against one another and assigned the outcome of every encounter a number of points similar to the number of years in gaol offered to Mike and Clyde by the District Attorney.

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This article was first published on Wiser Every Day.

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About the Author

Emeritus Professor Steven Schwartz AM is the former vice-chancellor of Macquarie University (Sydney), Murdoch University (Perth), and Brunel University (London).

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