The prisoner's dilemma (revised table)

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.

Axelrod found tournament participants adopted one of three general approaches to their strategies:

1. Always defect (the "best" strategy for a one-off encounter).

2. Always cooperate (and run the risk of losing out if your opponent decides to defect), or

3. Behave randomly (keep your opponent confused by cooperating or reneging unpredictably).

The simple strategy that led to the best overall outcome was called Tit for Tat. Tit for Tat always started by cooperating and then mimicked whatever its opponent did the last time they met. If an opponent reneges, Tit for Tat reneges on the next occasion. If the opponent cooperates, Tit for Tat cooperates in return.

The tournament also trialled several variations of Tit for Tat. Tit for Two Tats is a charitable strategy. It almost always cooperates and only retaliates when the opponent has defected twice in a row. Two Tits for Tat, on the other hand, is a severe strategy that punishes every defection with two of its own. Neither of these two variations did as well as the simple version of Tit for Tat.

One reason the Tit for Tat strategy is so successful is its consistency. Opponents learn quickly how it will behave. This does not mean that Tit for Tat is always the "best" strategy. Because Tit for Tat imitates what the opponent did last, it performs poorly when facing an opponent who always defects. To foster good outcomes, players must adopt a strategy that works with what their opponent is doing.

Like much of social life, the relations among countries require both cooperation and competition. All states put their interests first, but sometimes a nation's interests may best be protected by advancing the interests of others. For example, less hoarding and more sharing of Covid-19 vaccines would have slowed the rapid spread of Covid-19, saving lives not only in poorer countries but also by reducing the risk of new variants which affect all countries, including wealthy ones.

Although all tournament players had a chance to refine their strategies, a repeat of Axelrod's tournament produced exactly the same outcome. Tit for Tat was again the best strategy. Based on the two tournaments, Axelrod identified four rules for social interactions:

1. Cooperating often encourages others to do likewise. So, always start with cooperation, and continue to cooperate as long as your opponent does.

2. To discourage selfish behaviour, retaliate immediately for any unprovoked betrayal.

3. Forgive easily and return to cooperation.

4. Always be predictable so that others will know how you will respond to their behaviour.

The Prisoner's dilemma transcends politics; it is a moral rather than a legal issue. According to Axelrod, Tit for Tat won the tournaments even though it could never do better than the player it was interacting with. That is, it won by eliciting cooperation to create win-win outcomes The lesson is clear; if you want to get on in life, always start by being nice to others; forgive traitors, but don't be a pushover.