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."

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.

Quantifying the price of anarchy has given the field a concrete and rigorous way to assess the pros and cons of decentralized systems, which has broad implications across any number of domains where people find themselves involved in game-playing (whether they know it or not). A low price of anarchy means the system is, for better or worse, about as good on its own as it would be if it were carefully managed. A high price of anarchy, on the other hand, means that things have the potential to turn out fine if they're carefully coordinated-but that without some form of intervention, we are courting disaster. The prisoner's dilemma is clearly of this latter type. Unfortunately, so are many of the most critical games the world must play.

In fact, this makes defection not merely the equilibrium strategy but what's known as a dominant strategy. A dominant strategy avoids recursion altogether, by being the best response to all of your opponent's possible strategies-so you don't even need to trouble yourself getting inside their head at all. A dominant strategy is a powerful thing.

But now we've arrived at the paradox. If everyone does the rational thing and follows the dominant strategy, the story ends with both of you serving five years of hard time-which, compared to freedom and a cool half million apiece, is dramatically worse for everyone involved. How could that have happened?

This has emerged as one of the major insights of traditional game theory: the equilibrium for a set of players, all acting rationally in their own interest, may not be the outcome that is actually best for those players.

Algorithmic game theory, in keeping with the principles of computer science, has taken this insight and quantified it, creating a measure called "the price of anarchy." The price of anarchy measures the gap between cooperation (a centrally designed or coordinated solution) and competition (where each participant is independently trying to maximize the outcome for themselves). In a game like the prisoner's dilemma, this price is effectively infinite: increasing the amount of cash at stake and lengthening the jail sentences can make the gap between possible outcomes arbitrarily wide, even as the dominant strategy stays the same. There's no limit to how painful things can get for the players if they don't coordinate. But in other games, as algorithmic game theorists would discover, the price of anarchy is not nearly so bad.

For instance, consider traffic. Whether it's individual commuters trying to make their way through the daily bumper-to-bumper, or routers shuffling TCP packets across the Internet, everyone in the system merely wants what's easiest for them personally. Drivers just want to take the fastest route, whatever it is, and routers just want to shuffle along their packets with minimal effort-but in both cases this can result in overcrowding along critical pathways, creating congestion that harms everyone. How much harm, though? Surprisingly, Tim Roughgarden and Cornell's Eva Tardos proved in 2002 that the "selfish routing" approach has a price of anarchy that's a mere 4/3. That is, a free-for-all is only 33% worse than perfect top-down coordination.

Roughgarden and Tardos's work has deep implications both for urban planning of physical traffic and for network infrastructure. Selfish routing's low price of anarchy may explain, for instance, why the Internet works as well as it does without any central authority managing the routing of individual packets. Even if such coordination were possible, it wouldn't add very much.

Simple games like rock-paper-scissors may have equilibria visible at a glance, but in games of real-world complexity it's now clear we cannot take for granted that the participants will be able to discover or reach the game's equilibrium. This, in turn, means that the game's designers can't necessarily use the equilibrium to predict how the players will behave. The ramifications of this sobering result are profound: Nash equilibria have held a hallowed place within economic theory as a way to model and predict market behavior, but that place might not be deserved. As Papadimitriou explains, "If an equilibrium concept is not efficiently computable, much of its credibility as a prediction of the behavior of rational agents is lost." MIT's Scott Aaronson agrees. "In my opinion," he says, "if the theorem that Nash equilibria exist is considered relevant to debates about (say) free markets versus government intervention, then the theorem that finding those equilibria is [intractable] should be considered relevant also." The predictive abilities of Nash equilibria only matter if those equilibria can actually be found by the players. To quote eBay's former director of research, Kamal Jain, "If your laptop cannot find it, neither can the market."

We've all had the experience of talking to someone whose eyes drifted away-to their phone, perhaps-making us wonder whether our lackluster storytelling was to blame. In fact, it's now clear that the cause and effect are often the reverse: a poor listener destroys the tale.

Understanding the exact function and meaning of human backchannels continues to be an active area of research. In 2014, for instance, UC Santa Cruz's Jackson Tolins and Jean Fox Tree demonstrated that those inconspicuous "uh-huhs" and "yeahs" and "hmms" and "ohs" that pepper our speech perform distinct, precise roles in regulating the flow of information from speaker to listener-both its rate and level of detail. Indeed, they are every bit as critical as ACKs are in TCP. Says Tolins, "Really, while some people may be worse than others, 'bad storytellers' can at least partly blame their audience." This realization has had the unexpected side effect of taking off some of the pressure when he gives lectures-including, of course, lectures about that very result. "Whenever I give these backchannel talks, I always tell the audience that the way they are backchanneling to my talk right now is changing what I say," he jokes, "so they're responsible for how well I do."