The Prisoner’s Dilemma

A lesson in both the power and the limitation of models

Craig Axford
Aug 20, 2018 · 9 min read

“You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I’ll see to it that you both get early parole. If you both remain silent, I’ll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.” ~ Stanford Encyclopedia of Philosophy

In January of this year, I wrote an article entitled Human Beings Are Wired For Morality. Some who responded to that article took it as a deterministic argument for a kind of innate moral sense programmed into us by our genes, while others treated it as evidence for a supreme being. It wasn’t intended as either.

Cooperation has been and continues to be fundamental to our success as a species. From social bonds like friendships that involve two or more people to societies with thousands or even millions of members acting together to forge and maintain entire civilizations, cooperation is key.

While undoubtedly genetics does play a role in the emergence of and subsequent sophistication of our social relationships, the word “wired” in my January article was meant as a metaphor rather than as a technical description of what’s actually going on within our brains. Both genes and the environment will necessarily drive the evolution of social tendencies in any creature, but the moral sense that arises with these tendencies is merely an inevitable byproduct of them.

The word social, therefore, should be taken as being synonymous with cooperation and all the moral baggage it brings with it. Whether we are talking about a tribe getting ready to go to war, a gang planning the robbery of a convenience store, a family, or a government formulating and implementing policy, cooperation, for better or for worse, lies at the root of all of it.

Likewise, the conundrum commonly known as the prisoner’s dilemma reflects our penchant for forming cooperative relationships and the inevitable trade-offs they demand from us. Though the dilemma is set in a jail and involves two individuals arrested on suspicion of a crime, the moral challenge it describes really has nothing to do with what the prisoners in the thought experiment are accused of doing. That always remains unsaid. It involves questions of trust, self-interest, loyalty, and betrayal. In other words, this at first seemingly simple problem actually goes to the heart of what it means to be human.

As of this writing, The Stanford Encyclopedia of Philosophy page for the prisoner’s dilemma lists 20 major permutations that have been developed since “Puzzles with the structure of the prisoner’s dilemma were devised and discussed by Merrill Flood and Melvin Dresher in 1950, as part of the Rand Corporation’s investigations into game theory.” The Rand Corporation’s interest in game theory was motivated by the emerging potential for a global nuclear war.

As the description provided at the opening of this article states, the dilemma arises because there’s an inherent tension between the options being given to the prisoners in the thought experiment. Each suspect has the option of selling out the other in exchange for the possibility of going free. If one suspect squeals and the other remains silent, it’s the silent partner that will do hard time. If each of them rat out the other, they’ll both face punishment but with a chance for early parole. If neither says a word then the prosecutor’s lack of strong evidence means they’ll get a short sentence on a minor firearms possession charge.

At first glance, pointing the finger at the other guy is the best choice, until one realizes the other guy may very well be thinking the same thing. If so, both prisoners face a longer sentence than they would if they both just kept their mouth shut. But maybe prisoner A thinks prisoner B is loyal to a fault, and so selling out B isn’t so risky for A. Clearly, even in such a relatively straightforward case as this, each prisoner requires a theory of mind — a capacity to imagine what the other prisoner may be thinking and why he may be thinking it — to have the best chance at navigating the choices the problem presents to the most desirable outcome, at least if we assume each prisoner’s interests extend no further than gaining their freedom.

Whether we find it relatively easy or difficult to come up with a solution to the original 1950 prisoner’s dilemma, the truly important problems that life confronts us with are rarely so sharply defined. That’s why game theorists have developed so many permutations of it since. Each has been applied to a variety of problems ranging from complex social interactions to evolutionary biology in an effort to determine the best strategies in every case. In the process, additional variables have been added to facilitate a more accurate accounting of reality.

For social scientists, one issue they confront with any version of the dilemma is the problem of salience. How people, and to at least some degree other social creatures as well, evaluate the importance of their relationships with others is a variable that eludes easy quantification. Loyalty, for example, might be a cherished virtue to one or both of the prisoners, but how important will also depend a great deal upon the strength of the connection between the two prisoners confronting the dilemma. Prisoner A may be more loyal than your average person under any circumstance, but much more so if prisoner B is a close friend or relative.

This brings us to the fact that most social interactions actually defy simple algorithmic assessment. To put it another way, dilemmas don’t occur in a vacuum the way the prisoner’s dilemma, in all its forms, could mistakenly lead us to believe. Prisoner B’s thinking isn’t just informed by her relationship with prisoner A. She might not even particularly like prisoner A. But someone she does have a meaningful relationship with may be particularly fond of prisoner A, causing her to think more carefully about any action that would directly impact prisoner A than pure rational self-interest alone would normally trigger.

Indeed, we’ll never find just two prisoners in the room even if they’re the only people we can see. Our social networks go far beyond our particular friendships, mate choices, business partnerships, etc. They exist in a contextual stew that includes variables ranging from our own individual values and goals to how we think our actions will be perceived by others when they learn of our choice. Maybe I know the other prisoner well enough to feel certain he would never snitch on me. In addition, I may not give a fig about him and couldn’t care less if he spent the rest of his life in prison. But I also have my reputation to think about and people whose opinion matters to me will know I took advantage of the other prisoner’s sense of loyalty so that I could go free. No matter how robust the models that scientists and philosophers come up with are, plugging each of these personal considerations into them is impossible because they aren’t precisely the same for any two people.

That said, a social scientist would at this point probably remind us that the word social is used to describe their work for a reason. What the models are designed to do is find the best strategies on average for coping with life’s real dilemmas. Thought experiments like the prisoner’s dilemma are merely means to that end.

These models typically assume sufficiently large populations and run their simulations over multiple generations to test every possible outcome and determine which strategy wins out eventually. Even the winning strategy will produce a number of individual losers, but it will produce relatively fewer of them than the alternatives. The particulars that complicate each individual’s experience of the actual or proxy dilemmas being modeled dance around the average outcomes produced like guests at an outdoor wedding reception whirling around the pole at the center of the tent set up for the evening’s festivities.

In their recent documentary on the Vietnam War, the filmmakers Ken Burns and Lynn Novik spent a good deal of time discussing the United States Government’s focus on the number of North Vietnamese and Viet Cong killed and the ratio of enemy fatalities to American deaths in any given period. This emphasis on the body count incentivized brutality, often leading US commanders to order their soldiers to take out villages or to engage any human they encountered in particular parts of the country without first determining whether their targets were combatants. It also resulted in a number of Vietnamese casualties being counted as combatants after the fact when in truth they were not.

In episode 4 of the 10-part documentary, an army adviser observes wistfully, “If you can’t count what’s important, then you make what you can count important.” In the case of the Vietnam War, linear quantitative thinking not only had the tragic effect of needlessly maximizing the death toll but blinded military and other government officials to the historical and cultural context in which they were doing it. The consequence of using the wrong metric to measure America’s “progress” — or perhaps the assumption that a right metric could even be found in the first place — prolonged the Vietnam conflict and made US success even less likely than it was to begin with.

The Vietnam War is a stark and tragic reminder of what can happen when we substitute formulas and quantification for reality. Both the physical and social sciences necessarily rely upon these tools to clarify the problems they are attempting to address, but when we mistake our charts and graphs for the thing they are describing we are mistaking the map for the terrain. Models are an extremely valuable means for narrowing the gaps in our knowledge, but they will never close them. Knowledge is asymptotic.

Mistaking our maps for the territories they describe is particularly problematic in the context of the social sciences. Among other errors, it leads us to adopt simplistic essentialist views of human nature that have so far consistently missed the mark. This historic and ongoing failure of essentialism to successfully reduce the human condition to any single quantifiable trait or distinct set of traits has led many thinkers to the opposite and even more mistaken view that we are blank slates.

In their recent article There’s No Philosophy of Life Without a Theory of Human Nature, the philosophers Skye C Cleary and Massimo Pigliucci remind us that the elusive nature of the human condition is not an argument for seeing ourselves as blank slates as many would have it. They conclude:

If we were truly tabulae rasae, why would we prefer certain things to others? What could possibly urge us to seek meaning, to build relationships with other people, to strive to improve ourselves and the world we live in? We do all that because we are a particular kind of intelligent social animal, just as the Stoics thought. And we do it within the broad constraints imposed by our (biological as well as contingent) facticity, as the existentialists maintained. There is no single path to a flourishing human life, but there are also many really bad ones. The choice is ours, within the limits imposed by human nature.

The prisoner’s dilemma, in all its present and no doubt future permutations, is a useful tool for thinking about the choices we face “within the limits imposed by human nature.” It invites us to consider the difficult decisions life presents us with within the context of our self-interest, our social relationships with others, and our biological constraints. Over the years it has provided us with models that have been used to improve our understanding of how cooperation likely emerged as well as insights into our own personal and collective biases.

However, like all models, its capacity to enlighten will forever be limited because our own complexity and that of the environment in which we live is not only too vast to ultimately grasp in its entirety but too fluid. The process of acquiring an understanding of the social and physical world we inhabit changes the very nature of that world. It is the ambiguity inherent in the dilemma itself that ultimately rests at the heart of our reality. Progress depends not upon resolving that ambiguity, but wrestling with it.

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The Sensible Soapbox

We strive to produce content that provokes conversation of a political/social nature. Our goal is to increase insight and understanding in our communities.

Craig Axford

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US citizen residing in British Columbia, Canada. Degrees include anthropology and environmental studies. Activism, politics, science, nature.

The Sensible Soapbox

We strive to produce content that provokes conversation of a political/social nature. Our goal is to increase insight and understanding in our communities.