By Lambert Strether of Corrente.
For those who came in late, here’s an explanation of The Prisoner’s Dilemma (PD):
Albert W. Tucker formalized the game with prison sentence rewards and gave it the name “prisoner’s dilemma” (Poundstone, 1992), presenting it as follows:
- Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent. Here’s how it goes:
- If A and B both betray the other, each of them serves 2 years in prison
- If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
- If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
It’s implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision won’t affect their reputation in future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other.
Sorry to use Wikipedia, but it seems to be the best of the lot on the web, including Princeton’s obituary of Tucker, which describes PD’s ubiquity:
Tucker’s simple paradox has since given rise to a vast literature in subjects as diverse as philosophy, biology, sociology, political science, and economics, as well as game theory itself.
One important application of PD is found in Garrett Hardin’s extremely influential “Tragedy of the Commons” (Science162, 1243-1248 (1968)):
The tragedy of the commons develops in this way. Picture a pasture open to all. It is to be expected that each herdsman will try to keep as many cattle as possible on the commons. Such an arrangement may work reasonably satisfactorily for centuries because tribal wars, poaching, and disease keep the numbers of both man and beast well below the carrying capacity of the land. Finally, however, comes the day of reckoning, that is, the day when the long-desired goal of social stability becomes a reality. At this point, the inherent logic of the commons remorselessly generates tragedy.
As a rational being, each herdsman seeks to maximize his gain. Explicitly or implicitly, more or less consciously, he asks, “What is the utility to me of adding one more animal to my herd?” This utility has one negative and one positive component.
1) The positive component is a function of the increment of one animal. Since the herdsman receives all the proceeds from the sale of the additional animal, the positive utility is nearly +1.
2) The negative component is a function of the additional overgrazing created by one more animal. Since, however, the effects of overgrazing are shared by all the herdsmen, the negative utility for any particular decision-making herdsman is only a fraction of -1.
Adding together the component partial utilities, the rational herdsman concludes that the only sensible course for him to pursue is to add another animal to his herd. And another; and another… But this is the conclusion reached by each and every rational herdsman sharing a commons. Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit–in a world that is limited. Ruin is the destination toward which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons. Freedom in a commons brings ruin to all.
(Hardin, though citing to game theory sources, does not use the term PD explicitly. However, the payoff matrix for cooperation vs. defection is the same, as is the outcome of the game.) QED, right? Not so fast.
It’s interesting to note that when social scientist got around to — quelle horreur — actually testing Prisoner’s Dilemma on real prisoners, PD (and by extension not only Tucker’s thesis, but Hardin’s “tragedy”) broke down:
For six decades, the classic cooperation test known as the prisoner’s dilemma has been a mainstay of graduate courses on game theory and behavioral economics, not to mention in Hollywood detective series.
Until recently, no one thought to test the game on actual prisoners.
A pair of German economists offered female prisoners a chance, and found they were more likely to act in cahoots than shaft the other prisoner, compared with female students in a control group, according to a study published in the August edition of the Journal of Economic Behavior & Organization.
Ostrom, critiquing Hardin, explains why in her Nobel Lecture, which is dense but fast-moving and well worth reading and study:
The classic assumptions about rational individuals facing a dichotomy of organizational forms and of goods hide the potentially productive efforts of individuals and groups to organize and solve social dilemmas such as the overharvesting of common-pool resources and the underprovision of local public goods. The classic models have been used to view those who are involved in a Prisoner’s Dilemma [PD] game or other social dilemmas as always trapped in the situation without capabilities to change the structure themselves. This analytical step was a retrogressive step in the theories used to analyze the human condition. Whether or not the individuals who are in a situation have capacities to transform the external variables affecting their own situation varies dramatically from one situation to the next. It is an empirical condition that varies from situation to situation rather than a logical universality. Public investigators purposely keep prisoners separated so they cannot communicate. The users of a common-pool resource are not so limited.
When analysts perceive the human beings they model as being trapped inside perverse situations, they then assume that other human beings external to those involved – scholars and public officials – are able to analyze the situation, ascertain why counterproductive outcomes are reached, and posit what changes in the rules-in-use will enable participants to improve outcomes. Then, external officials are expected to impose an optimal set of rules on those individuals involved. it is assumed that the momentum for change must come from outside the situation rather than from the self-reflection and creativity of those within a situation to restructure their own patterns of interaction.
So, whenever you hear an analyst or expert, especially an economist, invoke the Prisoner’s Dilemma, you might ask yourself, this being the hermeneutic part:
1) Whether the key assumption — that game participants cannot communicate — is realistic* in context as you know it, and
2) Whether — and here we draw on the seminal work by Outis Philalithopoulos on “academic choice theory” — the analyst or expert is personally invested in the “optimal set of rules” they will seek to impose on you (and people like you).
Indeed, considered in this light, “rationality,” as our economists understand it, looks an awful lot like mere compliance to a dehumanizing denial of agency.
NOTE One cannot help but wonder whether academic politics was an effective forcing ground for PD and game theory generally because its communication channels are so clogged with bullshit they might as well not exist. Frank Herbert, The Tactful Saboteur:
Two practitioners of the art of mental healing, so the story goes, passed each other every morning on their way to their respective offices. They knew each other, but weren’t on intimate terms. One morning as they approached each other, one of them turned to the other and said, “Good morning.” The one greeted failed to respond, but continued toward his office. Presently, though he stopped, turned and stared at the retreating back of the man who’d spoken, musing to himself: “Now, what did he really mean by that?”