...Archive for February 2022

The real prisoners’ dilemma

The prisoners’ dilemma is our goto example for a sort of gigantic sigh. Everything these days, we say, is a "coordination problem”. In the prisoners' dilemma, a prosecutor separates two alleged collaborators in a crime, and demands that each confess. If one confesses and helps to prosecute the other, the snitch will be set free while the hold-out will be punished very severely. If neither confesses, they both get off with a slap on the risk. If both confess, they'll both be put away, but not for quite as long as if one had held out and got busted. The gigantic sigh is that even though the prisoners’ common interest would best be served by both agreeing to hold out, absent any ability to coordinate, the narrowly rational choice for each prisoner is to confess. If the other guy isn’t gonna confess, and I do, then I get off, which is better than a slap on the wrist. If the other guy is gonna confess, and I do too, that’s better than the very severe punishment I'd receive if I hold out and let the other guy's confession damn me. So the outcome is both prisoners confess and are put away, even though both would have been better off if they’d held their tongues. Sigh. Alas.

It seems like every bad thing can be described as a prisoners’ dilemma. We’d all be better off, for example, if the world didn’t warm into a post-apocalyptic hellscape. But each of us gains a lot from our own activities that spew carbon into the atmosphere, and the probability of post-apocalyptic hellscape is not meaningfully diminished by our individual abstentions. So, for each of us individually, the rational thing is to keep on spewing. So we all do that, and the result is collective catastrophe. Sigh. There are things the government could do that would really make our lives better. But for politicians of either political party, the benefit to the country of a popular good thing is diffuse relative to the electoral disadvantage they would experience if the good thing happened under the other party’s leadership. So for each party, the narrowly rational choice is to block good things while the other party leads. The equilibrium is gridlock, good things left undone, unnecessary misery for all. Sigh.

In the unlikely event, dear interfluidity reader, that it was not old hat to you, you probably bristled a bit at my account of the original prisoners’ dilemma. Yes, sure, from a very narrow perspective it might make sense for each prisoner to snitch. But if the prisoners know each other and will encounter one another again, the difference between getting off entirely and a slap on the risk probably wouldn’t be worth the blowback. Maybe the other guy is gonna put a shiv in my belly. Maybe I’ll just lose a friend. Either way might be enough to shift my choice. The canonical prisoners' dilemma seems artificial, implausible. Theoreticians have to clarify that the certain bad outcome they predict holds only in a “one-shot" game. In a more natural “repeated” or “iterated" game, the prisoners might well keep their mouths shut. And that points to the problem with the prisoners’ dilemma as an intuition pump.

Human beings are fantastic coordinators. Almost everything we do involves coordinating with others, often without any kind of explicit agreement to do so. In many situations we empathetically place ourselves in the position of strangers, and do the right thing by them even at cost to ourselves. Why do you clean up after yourself at a picnic table hidden in some unsurveilled grove? Where there might be large rewards to collective action, we have developed extraordinarily contingent and detailed tools — contract law, formal organizations, states — to coordinate effectively. The prisoners’ dilemma in its cliché telling smuggles in an assumption that noncoordination is the default, that our prisoners will behave like selfish atoms absent a formal bond. But that’s not how humans are. Coordination spurts from us like a mutant weed, intertwining our behavior with others as soon as we encounter them, even if only imaginatively.

But the prisoners’ dilemma story is not so unrealistic in its particular context. Prosecutors really can get prisoners to confess by setting up these kinds of games! But note the active voice. The dilemma doesn’t just happen. Prosecutors frame the situation. They isolate the prisoners. They suggest the other guy is going to “play ball” in order to impair the expectations any tacit coordination would rely upon.

In real life, the prisoners’ dilemma doesn’t result from some anodyne “coordination failure”. The real prisoners' dilemma is a setup. More charitably, we can understand it as a battle between competing teams of coordinators. Police and prosecutors coordinate to apprehend the alleged criminals, to divide them in spaces that prevents coordination through overt communication, to carefully manage the information to which they are exposed in order to shape their behavior towards the self-interested, isolated actors presumed by a one-shot prisoners' dilemma. The prisoners — before their apprehension, tacitly or overty; during their ordeal itself tacitly; by virtue of expectations they may have arranged for the future — strive to coordinate in order to avoid their mutual imprisonment. If they are actually innocent, hopefully protestation of innocence becomes a strong Schelling point to coordinate upon. (There is no guarantee of that. The conventional logic and expected equilibrium are not altered by actual innocence.)

Coordination rarely just "fails". Almost always, what we call coordination failure results from one group of potential coordinators being outcoordinated by another group, under circumstances where the two groups’ interests diverge. High quality coordination is the human default, but we very often coordinate with one another to frustrate rival groups' ability to coordinate, to create coordination failures, in order to more easily achieve our own goals. Police and prosecutors isolate and seek to undermine the trust between prisoners. Antitrust authorities seek to hinder and punish certain kinds of coordination between firms. Fossil fuel interests work to undermine any consensus surrounding the likely course of climate change, in order to prevent that from becoming a basis of coordination against their interest by other parties. Partisan gridlock and civic strife are financed by interests who see more threat than opportunity in an effective, active state. The flames are fanned by interests who see more opportunity than threat in replacing civil society with entertainment. Red tribe / blue tribe, woke / antiwoke — these are strategic outcomes, not emergent phenomena. We fail to “pull together” because factions are coordinating excellently to divide us.

I often encounter a sentiment, especially among tech types, that coordination failure is at the root of all evil. If only we had better tools, new coordination devices, the theory goes, a lot of social ills might be solved. I think that misdiagnoses the problem. “Coordination failure” is a blessing at least as often as it is a curse. I am in favor of the coordination failures that help keep product markets competitive. I am in favor of police and prosecutors outcoordinating organized criminals (although I want them to do so in a way that frustrates the coordination of the guilty without conspiring to put away the innocent). I am in favor of criminalizing coordination between judges with litigants. I am in favor of journalists and whistleblowers outcoordinating well organized regimes of government and corporate secrecy when information in the public interest is being concealed. There would be no political stability if the coordination equilibrium that is the bedrock of any government’s authority were very easy to coordinate out of to some next shiny thing.

The evils for which we hold “coordination failure” responsible are not attributable to some sad theorem of game theory. We could say instead that they are caused by bad actors — the fossil fuel interests that frustrate our ability to coordinate against global warming, the plutocrats who create incentives to entrench partisan gridlock. But that is I think too easy, and often counterproductive. The root problem is divergence of interest itself.

Obviously, in any polity or human community, there will always be some divergence of interest. No two humans' requirements or yearnings are perfectly alike. But in some polities, the welfare of the community as a whole overwhelms whatever differences of station jockeying among subgroups might yield. In our society, differences of outcome within are so great, and broad social improvement so implausible, that coordinating competitively over our place in the distribution seems more fruitful than coordinating cooperatively to improve the distribution.

Until we remedy that, expect a lot of “coordination failures”. In the real prisoners’ dilemma, we are all one another’s prisoners, and one another’s prosecutors. We have better things to do.