Prisoners all

Decisions, decisions

Two suspects are arrested after a series of armed robberies. They are interrogated separately, and each is offered the following deal: Confess and testify against your partner and you’ll get five years in prison. Stay silent and you’ll get twenty-five. But there is a condition: You have to be the first to take the offer. If your partner beats you to it, the offer is withdrawn.

Suspect Abel thinks it over. The cops wouldn’t make this offer if they had solid evidence against us; they need a confession. If we both keep quiet, we might get off entirely. So maybe I should keep quiet.

Suspect Baker thinks the same thing. 

But they can’t communicate, and neither trusts the other. Abel’s second thoughts tell him to confess and testify, and do it quickly. That way he’ll get only five years. Otherwise he risks twenty-five. So he confesses and testifies against Baker.

Baker reasons along similar lines. And so he confesses and testifies against Abel.

With both confessions, the police quickly close the case. They generously call a tie between Abel and Baker, and the two go to prison for five years.

In his prison cell, Abel wonders if he could have done better. If they had both kept quiet, they would both be free. Baker should have realized this.

But there was that distrust between the two. Given that, they couldn’t have done better. And five years in prison is better than twenty-five.

The problem confronting Abel and Baker is a version of the prisoner’s dilemma, a mainstay of game theory since that hybrid of economics and political science emerged in the 1950s. The version given here is simpler and more realistic (from a cops-and-robbers standpoint) than some other versions, which specify consequences that more rigorously compel each crook to rat on the other.

But all make the same point about decision-making: It’s hard when the interests of the decision-makers align imperfectly. If the interests align perfectly—if my gain is your gain, and vice versa—then cooperation is the obvious choice. If the interests don’t align at all—as in a zero-sum game, where my gain is your loss—then opposition is the only reasonable option.

In the real world, imperfect alignment is ubiquitous. Parents’ interests align imperfectly with those of their children. The parents want the best for the kids, but they have to keep their own interests partly in mind, lest in sacrificing themselves they cause the kids to suffer. If a mother robin forgets to eat, she can’t keep feeding her nestlings for long.

The interests of allies in war typically align imperfectly. America, Britain and Russia all wanted to defeat Germany in World War II. But America wanted to spread democracy (up to a point), while Britain sought to preserve its empire and Russia aimed to promote communism and create a buffer zone on its western flank. The diplomacy of the Grand Alliance reeked of the distrust of the leaders of the three countries for each other. Stalin suspected Roosevelt and Churchill of delaying their invasion of French so Soviet troops would do most of the dying in the fight against Hitler. Churchill suspected Roosevelt of wanting to spring India from the British empire. Roosevelt was sure Stalin had evil designs on Poland and Eastern Europe.

The interests of countries engaged in trade align imperfectly. Most countries acknowledge that trade conveys benefits in terms of access to goods produced more efficiently elsewhere; but most also reckon that trade entails costs to particular sectors of their economies, and that it renders them susceptible to foreign influence. Taiwan makes the best semiconductors in the world, but America’s reliance on them does harm to America’s semiconductor industry and raises the stakes in case China tries to seize Taiwan.

Negotiations over climate change exhibit a similar imperfect alignment of interests. Everyone benefits from global reductions of carbon emissions. But costs are higher in some countries than in others, and benefits vary as well. And here the lack of trust is a big barrier to change. However reliable a country’s government might seem as a negotiating partner, that government might be replaced by one with different priorities. Meaningful change on climate issues takes a long time; who is willing to trust other countries over such a stretch?

So what is to be done? How is the prisoner’s dilemma to be resolved?

Game theorists offer variants of the dilemma, including versions that allow repetition. In these the prisoners can learn from each other and develop expectations. Trust—of a self-interested sort—can arise. 

This is exactly how the real world operates. We get to know others, and some we learn to trust. With them we can achieve better outcomes.

But it’s not easy, and we make mistakes. In the end, there’s no way around the fact that we’re all prisoners—of constraints on choice—even if we’re not all criminals.