The Threat That Leaves Something to Chance

In the 1955 James Dean movie Rebel Without A Cause, two cars race toward each other for a head-on collision. The first driver who swerves out of the way is the “chicken” and loses face. But if neither swerve, they both face catastrophe. That’s why game theorists call this kind of situation “the game of chicken”.?

It’s different in important ways from the other commonly known game model, the Prisoner’s Dilemma. The most important difference isn’t really about what’s called the “payoff structure” that determines what winners and losers receive when the game ends.? It is the communication and “audience costs” that the games involve.?

In Prisoner’s Dilemma, the two accused criminals who partnered in a crime are kept in separate interrogation rooms and cannot communicate. Each is told by the district attorney that if they squeal and give up the other, they will get a shortened jail sentence in return, while the other will go to jail for a long time.?

The game is interesting precisely because in order to get to the best outcome for both (mutual cooperation, where neither gives up the other and the DA cannot convict) they have to coordinate their behavior without communicating. If they are playing only once (what’s called a single shot game) and have a high discount rate (the future matters very little relative to the present) there is only one equilibrium outcome in the Prisoner's Dilemma: mutual defection. Both criminals implicate the other, and both end up spending more time in jail than either would if they had kept quiet.

The game of chicken, on the other hand, is all about communication. The movie scene has two testosterone-fueled 1950s male teenagers with muscle cars and a bunch of friends (and both real and potential girlfriends) watching. Before the game starts, there’s trash-talking –– both at each other and to the audience (audience costs are just a game theoretic terms for the ridicule and longer term loss of credibility and status that the loser will face from all the friends, after they swore to everyone that they’d rather die than swerve). Once they’re in the cars, there’s engine-revving and brake squealing. When they’re aiming at each other, both are trying to see into the eyes and facial expression of the other; and both are doing everything they possibly can to show no fear.?

Surely they're afraid.? But the more a player succeeds in the deception, the more likely he is to win.

Recognize the dynamics of the debt-ceiling negotiations? As happens frequently in politics and business, we’re watching a game of chicken played out live, with a default on U.S. Treasury debt the catastrophic outcome we’ll suffer if neither party swerves. The structure of the game makes much of what we’ve seen over the last few weeks –– and will surely continue to see –– utterly predictable. It’s inherent in the structure of the game, and not really a function of ideology or particular personalities or anything else distinctive to 2023.?

Both sides will increase their audience costs by promising more rigid policies to the constituents and stakeholders they value the most –– the point being precisely to increase the visibility to the other party of the massive costs they would suffer by backing down. Both will intentionally climb what deterrence theorists in the 1970s called “the ladder of escalation” — where the risk of catastrophe for everyone rises incrementally. The goal here is to discover just how much risk each side is actually willing to accept (and cut through the deception). When you get up to the rung of the ladder at which one side’s risk acceptance threshold is exceeded but the other’s is still higher up, you have a winner.?

Of course, before you get to that place, both sides really have no choice but to try to convince the other that they are willing to accept more risk than they actually are. If one succeeds in that deception, they win.

Enter Tom Schelling, the Nobel Prize winning economist who was one of the most important figures in the development of modern game theory and its application to decision making. In what is still one of the most valuable books on strategy ever written, his 1960 classic The Strategy of Conflict, Schelling breaks down the game of chicken (in simple plain English, not complicated math –– one of his great charms) with this elegant question: how do you win???

The answer in one sense is simple: you can guarantee a win in the game of chicken by throwing your steering wheel out the window. It’s the same logic as “burning your bridges behind you” to prove that you will not retreat from a fight... by making it physically impossible to do so. As long as the other party in the game sees you throw your steering wheel out the window, you win.??

In theory.?

In practice, it’s not that simple. How does the other party know that you don’t have an extra steering wheel hidden under your seat? Or maybe you’ve pre-engineered your tires so that the car will drift left or right by five degrees, just enough to avoid the collision and in a way that you can claim you didn’t actually show cowardice and back down?

This is where Schelling comes up with the more refined concept of "the threat that leaves something to chance". The best way to win at the game of chicken is actually not to throw your steering wheel out the window. It is to hand your steering wheel to a proverbial monkey who is sitting in the passenger seat next to you. The monkey doesn’t know what is going on, so it acts like a random number generator. It might itself throw the steering wheel out the window.? It might give it back to you and let you re-establish control of the car. It might sit there and do nothing. Its decision making is random.

Your adversary can’t predict what that monkey will do. And the whole point is, neither can you.? This kind of uncertainty –– that even the player creating it cannot resolve –– is actually the most effective way to increase the chances of a win.

So expect to see precisely this kind of dynamic play out in the coming days. Observers will say it makes no sense and that it’s irrational. But that’s the strategy. Later in his writings, Schelling coined the phrase “the rationality of irrationality” to describe what this looks and feels like. It is entirely rational –– in a strategic sense –– for both sides to try to convince the other that they are somewhat irrational in a decision making sense.??

An important caveat: politicians, like any negotiators, aren’t fully trapped by some law of nature in a game structure that they cannot escape. They could, in principle, engineer themselves out of the game of chicken and find a compromise that both can live with before they even really get in the cars to play the game. It’s not the most likely outcome though. And even with a threat that leaves something to chance, there is a non-trivial possibility that the other side misunderstands the size of that chance, or the magnitude of the catastrophe should the cars crash into each other.?

We could end up in a technical default on U.S. Treasury debt within the next several weeks, and the consequences for business and government on a global scale will be the subject of continued speculation in the interim. More likely, the game of chicken will end close to the last moment with a swerve that is larger on one side than on the other. And then the communications game will quickly switch to convincing the audience that it wasn’t really what it appeared to be.?

Playing the debt default game with a threat that leaves something to chance isn’t always fun to watch –– but that’s what the days ahead have in store.