Algorithms to Live By

by Brian Christian

  The logic of this type of game is so pervasive that we don’t even have to look to misdeeds to see it running amok. We can just as easily end up in a terrible equilibrium with a clean conscience. How? Look no further than your company vacation policy. In America, people work some of the longest hours in the world; as the Economist put it, “nowhere is the value of work higher and the value of leisure lower.” There are few laws mandating that employers provide time off, and even when American employees do get vacation time they don’t use it. A recent study showed that the average worker takes only half of the vacation days granted them, and a stunning 15% take no vacation at all.

  At the present moment, the Bay Area (where the two of us live) is attempting to remedy this sorry state of affairs by going through a radical paradigm shift when it comes to vacation policy—a shift that is very well meaning and completely, apocalyptically doomed. The premise sounds innocent enough: instead of metering out some fixed arbitrary number of days for each employee, then wasting HR man-hours making sure no one goes over their limit, why not just let your employees free? Why not simply allow them unlimited vacation? Anecdotal reports thus far are mixed—but from a game-theoretic perspective, this approach is a nightmare. All employees want, in theory, to take as much vacation as possible. But they also all want to take just slightly less vacation than each other, to be perceived as more loyal, more committed, and more dedicated (hence more promotion-worthy). Everyone looks to the others for a baseline, and will take just slightly less than that. The Nash equilibrium of this game is zero. As the CEO of software company Travis CI, Mathias Meyer, writes, “People will hesitate to take a vacation as they don’t want to seem like that person who’s taking the most vacation days. It’s a race to the bottom.”

  This is the tragedy of the commons in full effect. And it’s just as bad between firms as within them. Imagine two shopkeepers in a small town. Each of them can choose either to stay open seven days a week or to be open only six days a week, taking Sunday off to relax with their friends and family. If both of them take a day off, they’ll retain their existing market share and experience less stress. However, if one shopkeeper decides to open his shop seven days a week, he’ll draw extra customers—taking them away from his competitor and threatening his livelihood. The Nash equilibrium, again, is for everyone to work all the time.

  This exact issue became a flash point in the United States during the 2014 holiday season, as retailer after retailer, unwilling to cede market share to competitors who were getting ahead of the usual post-Thanksgiving shopping rush, caved in toward the lousy equilibrium. “Stores are opening earlier than ever before,” the International Business Times reported. Macy’s decided to open two hours earlier than the year before, as did Target. Kmart, for its part, opened at 6:00 a.m. on Thanksgiving morning, and was continuously open for forty-two hours.

  So what can we, as players, do when we find ourselves in such a situation—either the two-party prisoner’s dilemma, or the multi-party tragedy of the commons? In a sense, nothing. The very stability that these bad equilibria have, the thing that makes them equilibria, becomes damnable. By and large we cannot shift the dominant strategies from within. But this doesn’t mean that bad equilibria can’t be fixed. It just means that the solution is going to have to come from somewhere else.

  Mechanism Design: Change the Game

  Don’t hate the player, hate the game.

  —ICE-T

  Don’t ever take sides with anyone against the family again—ever.

  —THE GODFATHER

  The prisoner’s dilemma has been the focal point for generations of debate and controversy about the nature of human cooperation, but University College London game theorist Ken Binmore sees at least some of that controversy as misguided. As he argues, it’s “just plain wrong that the Prisoner’s Dilemma captures what matters about human cooperation. On the contrary, it represents a situation in which the dice are as loaded against the emergence of cooperation as they could possibly be.”*

  Well, if the rules of the game force a bad strategy, maybe we shouldn’t try to change strategies. Maybe we should try to change the game.

  This brings us to a branch of game theory known as “mechanism design.” While game theory asks what behavior will emerge given a set of rules, mechanism design (sometimes called “reverse game theory”) works in the other direction, asking: what rules will give us the behavior we want to see? And if game theory’s revelations—like the fact that an equilibrium strategy might be rational for each player yet bad for everyone—have proven counterintuitive, the revelations of mechanism design are even more so.

  Let’s return you and your bank-robbing co-conspirator to the jail cell for another go at the prisoner’s dilemma, with one crucial addition: the Godfather. Now you and your fellow thief are members of a crime syndicate, and the don has made it, shall we say, all too clear that any informants will sleep with the fishes. This alteration of the game’s payoffs has the effect of limiting the actions you can take, yet ironically makes it far more likely that things will end well, both for you and your partner. Since defection is now less attractive (to put it mildly), both prisoners are induced to cooperate, and both will confidently walk away half a million dollars richer. Minus, of course, a nominal tithe to the don.

  The counterintuitive and powerful thing here is we can worsen every outcome—death on the one hand, taxes on the other—yet make everyone’s lives better by shifting the equilibrium.

  For the small-town shopkeepers, a verbal truce to take Sundays off would be unstable: as soon as either shopkeeper needed some extra cash he’d be liable to violate it, prompting the other to start working Sundays as well so as not to lose market share. This would land them right back in the bad equilibrium where they get the worst of both worlds—they’re exhausted and don’t get any competitive advantage for it. But they might be able to act as their own don by signing a legally binding contract to the effect that, say, any proceeds earned by either shop on a Sunday go to the other shop. By worsening the unsatisfactory equilibrium, they’d make a new and better one.

  On the other hand, a change to the game’s payoffs that doesn’t change the equilibrium will typically have a much smaller effect than desired. The CEO of the software firm Evernote, Phil Libin, made headlines with a policy of offering Evernote employees a thousand dollars cash for taking a vacation. This sounds like a reasonable approach to getting more employees to take vacation, but from a game-theoretic perspective it’s actually misguided. Increasing the cash on the table in the prisoner’s dilemma, for instance, misses the point: the change doesn’t do anything to alter the bad equilibrium. If a million-dollar heist ends up with both thieves in jail, so does a ten-million-dollar heist. The problem isn’t that vacations aren’t attractive; the problem is that everyone wants to take slightly less vacation than their peers, producing a game whose only equilibrium is no vacation at all. A thousand bucks sweetens the deal but doesn’t change the principle of the game—which is to take as much vacation as possible while still being perceived as slightly more loyal than the next guy or gal, therefore getting a raise or promotion over them that’s worth many thousands of dollars.

  Does this mean that Libin needs to offer tens of thousands of dollars per employee per vacation? No. Mechanism design tells us that Libin can get the happy employees he wants with the stick, rather than the carrot; he can get a better equilibrium without spending a dime. For instance, he could simply make a certain minimal amount of vacation compulsory. If he can’t change the race, he can still change the bottom. Mechanism design makes a powerful argument for the need for a designer—be it a CEO, a contract binding all parties, or a don who enforces omertà by garroted carotid.

  A league commissioner is this kind of a designer as well. Imagine how pathetic a sight the NBA would be if there were no games as such, and teams could simply score on each other at literally any time between the start and end of the season: 3:00 a.m. on a Sunday, noon on Christmas,
you name it. What you’d see would be haggard, cadaverous players, in extreme sleep debt, forcing vigilance with chemical stimulants, almost losing their minds. War is like this. On the other hand, even Wall Street, ruthless cutthroat capitalists trading by the microsecond in the “city that never sleeps,” comes to a cease-fire every day at 4:00 p.m. sharp, so that brokers can sleep at predictable hours every night without getting too badly ambushed by competitors pushing toward a sleepless equilibrium. In this sense, the stock market is more a sport than a war.

  Scaling up this logic results in a potent argument for the role of government. In fact, many governments do have laws on the books mandating minimum vacations and limiting shop hours. And while the United States is one of the only developed nations without federal requirements for paid vacation, Massachusetts, Maine, and Rhode Island do have state-level prohibitions on Thanksgiving commerce.

  Laws like these often stem from the colonial era and were initially religious in nature. Indeed, religion itself provides a very direct way of modifying the structure of games of this kind. In particular, a religious law such as “Remember the Sabbath day” neatly solves the problem faced by the shopkeepers, whether enforced by an all-powerful God or by the more proximate members of a religious community. And adding divine force to injunctions against other kinds of antisocial behavior, such as murder, adultery, and theft, is likewise a way to solve some of the game-theoretic problems of living in a social group. God happens to be even better than government in this respect, since omniscience and omnipotence provide a particularly strong guarantee that taking bad actions will have dire consequences. It turns out there’s no Godfather quite like God the Father.

  Religion seems like the kind of thing a computer scientist rarely talks about; in fact, it’s literally the subject of a book called Things a Computer Scientist Rarely Talks About. But by reducing the number of options that people have, behavioral constraints of the kind imposed by religion don’t just make certain kinds of decisions less computationally challenging—they can also yield better outcomes.

  Mechanism Design by Evolution

  How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it, except the pleasure of seeing it.

  —ADAM SMITH, THE THEORY OF MORAL SENTIMENTS

  The heart has its reasons which reason knows nothing of.

  —BLAISE PASCAL

  The redwoods of California are some of the oldest and most majestic living things on the planet. From a game-theoretic standpoint, though, they’re something of a tragedy. The only reason they’re so tall is that they’re trying to be taller than each other—up to the point where the harms of overextension are finally even worse than the harms of getting shaded out. As Richard Dawkins puts it,

  The canopy can be thought of as an aerial meadow, just like a rolling grassland prairie, but raised on stilts. The canopy is gathering solar energy at much the same rate as a grassland prairie would. But a substantial portion of the energy is “wasted” by being fed straight into the stilts, which do nothing more useful than loft the “meadow” high in the air, where it picks up exactly the same harvest of photons as it would—at far lower cost—if it were laid flat on the ground.

  If the forest could only somehow agree to a kind of truce, the ecosystem could enjoy the photosynthetic bounty without the wood-making arms race wasting it all. But as we’ve seen, good outcomes in these scenarios tend only to arise in the context of an authority outside the game—someone changing the payoffs from the top down. It would seem as though in nature, then, there is simply no way of establishing good equilibria between individuals.

  On the other hand, if cooperation really does lead to better outcomes in certain games, then we’d expect that cooperatively minded species would prevail evolutionarily. But then where would the cooperation come from if it’s only rational at the group level, not the individual level? Maybe it would have to come from something that individuals can’t entirely control. Something, for instance, like emotions.

  Consider two seemingly unrelated scenarios: (1) A man buys a vacuum cleaner, it breaks within a few weeks, and he spends ten minutes online leaving a vindictive review. (2) A woman shopping at a convenience store notices someone steal an elderly man’s wallet and bolt for the door; she tackles the thief and wrestles the wallet free.

  Though the latter protagonist seems clearly heroic, and the former merely angry, what these vignettes have in common—albeit in very different ways—is involuntary selflessness. The unhappy consumer isn’t trying to get the vacuum cleaner replaced or his money back; he’s after a highly indirect kind of retribution, from which—in a rational, game-theoretic sense—he stands to gain little other than the spiteful satisfaction of writing the review itself. In the convenience store, the heroic woman metes out vigilante justice at enormous personal cost; she risks injury or even death to return, say, $40 to a man who is a total stranger to her. Even if she wanted to help, she could have simply taken two twenties out of her own pocket and given them to him without risking a trip to the ER! In this sense, both protagonists are acting irrationally. On the other hand, their actions are good for their society: we all want to live in a world in which pickpocketing doesn’t pay and in which businesses that sell poor-quality products get a bad reputation.

  Perhaps each of us, individually, would be better off being the kind of person who can always make a detached, calculated decision in their own best interest, not willing to lose time fuming over a sunk cost, let alone lose a tooth over $40. But all of us are better off living in a society in which such defiant stands are common.

  So what has acted up in these people, in the absence of an external authority, to make them buck the selfish equilibrium? Anger, for one thing. Whether prompted by a shoddy business or a petty thief, outrage can override rationality. And in these instances, it may be that the hand of evolution has done what it would otherwise have taken an authority outside the game to accomplish.

  Nature is full of examples of individuals being essentially hijacked to serve the goals of another species. The lancet liver fluke (Dicrocoelium dendriticum), for instance, is a parasite that makes ants deliberately climb to the tops of grass blades so that they’ll be eaten by sheep—the lancet fluke’s preferred host. Likewise, the parasite Toxoplasma gondii makes mice permanently lose their fear of cats, with similar results.

  Emotion, for the bitter, retaliatory consumer and for the convenience-store hero alike, is our own species taking over the controls for a minute. “Morality is herd instinct in the individual,” wrote Nietzsche. Paraphrasing slightly, we might hazard that emotion is mechanism design in the species. Precisely because feelings are involuntary, they enable contracts that need no outside enforcement. Revenge almost never works out in favor of the one who seeks it, and yet someone who will respond with “irrational” vehemence to being taken advantage of is for that very reason more likely to get a fair deal. As Cornell economist Robert Frank puts it, “If people expect us to respond irrationally to the theft of our property, we will seldom need to, because it will not be in their interests to steal it. Being predisposed to respond irrationally serves much better here than being guided only by material self-interest.”

  (Lest you think that civilized modern humans have legal contracts and rule of law instead of retribution, recall that it’s often more work and suffering to sue or prosecute someone than the victim could ever hope to recover in material terms. Lawsuits are the means for self-destructive retaliation in a developed society, not the substitute.)

  As for anger, so for compassion and guilt—and love.

  As odd as it might sound, the prisoner’s dilemma also has a lot to tell us about marriage. In our discussion of optimal stopping problems, such as the secretary problem, back in chapter 1, we looked at both dating and apartment hunting as cases where we must make a commitment with possible future o
ptions yet unseen. In both love and housing, though, we continue to encounter more options even after our optimal-stopping decision is made—so why not be ready to jump ship? Of course, knowing that the other party (be it spouse or landlord) is in turn prepared to jump ship would prevent many of the long-term investments (having children together, or laboriously moving in one’s belongings) that make those agreements worthwhile.

  In both cases this so-called commitment problem can be at least partially addressed by a contract. But game theory suggests that in the case of dating, the voluntary bonds of the law are less relevant to an enduring partnership than the involuntary bonds of love itself. As Robert Frank puts it, “The worry that people will leave relationships because it may later become rational for them to do so is largely erased if it is not rational assessment that binds them in the first place.” He explains:

  Yes, people search for objective characteristics they care about. Everybody wants somebody who’s kind and intelligent and interesting and healthy and maybe physically attractive, good earning power, the whole laundry list of features, but that’s the first pass.… After you’ve spent enough time together, it’s not those things that make you want to stay together. It’s just the fact that it’s that particular person—that is what’s valuable to you, so you don’t really need the contract so much as you need a feeling that makes you not want to separate, even though objectively there might be a better option available to you.

  Said differently: Love is like organized crime. It changes the structure of the marriage game so that the equilibrium becomes the outcome that works best for everybody.

  Playwright George Bernard Shaw once wrote of marriage that “If the prisoner is happy, why lock him in? If he is not, why pretend that he is?” Game theory offers a subtle answer to this particular riddle. Happiness is the lock.

  A game-theoretic argument for love would highlight one further point: marriage is a prisoner’s dilemma in which you get to choose the person with whom you’re in cahoots. This might seem like a small change, but it potentially has a big effect on the structure of the game you’re playing. If you knew that, for some reason, your partner in crime would be miserable if you weren’t around—the kind of misery even a million dollars couldn’t cure—then you’d worry much less about them defecting and leaving you to rot in jail.