Game Theory and the Debt Ceiling

Who's Game? (picture: Moyan Brenn,

Who’s Game?

The idea of applying game theory to the debt ceiling debate isn’t exactly new. In fact, I did exactly that, back in March. The FT just ran an article on that very concept.

Quoting my March post: “taking hostages doesn’t work if you are known to waive self-imposed ultimatums”. Herein lies the problem: Game theoretically, the Debt Ceiling debate is a game of chicken. And a repeated game of chicken is not stable. Let me explain.

We would all like to assume that people ultimately do the ‘right’ thing (i.e. they cooperate). And there is evidence that this often happens. But it does happen under very specific conditions. Robert Axelrod, one game theorist who has done a lot of work on cooperation and norms, names a few examples: The ‘Live-and-Let-Live’ system in trench warfare in WWI, for example. Soldiers from opposing sides started to cooperate. Whether that was the ‘right’ thing would of course depend on your vantage point.

It turns out that a necessary condition for repeated cooperation to occur is that the players repeatedly play with the same or similar opponents, and that they recognize that fact. The generals, who wanted the soldiers to re-engage in the killing business, stumbled on the ‘solution’ by accident: If you rotate the location of the units, they start shooting again! Once the solders didn’t face the same enemy every day, the ‘trust’ that either side won’t shoot to kill evaporated, and soldiers went on with their deadly duties.

While cooperation lasted, the artillery had a lot less to lose by attacking than the infantry, as they were mobile and didn’t stay in one place for long. So the forward observers of the artillery were ‘bribed’ by infantrymen with spare delicacies, and knew it was polite to ask if the infantry wanted them to cause trouble or not. Who doesn’t know the story of soldiers on both sides sharing Christmas dinner, or of the infantryman running out of his trench alone, over to the other side screaming apologies, saying that the artillery was to blame for a deadly shot, and not the infantry.

Although it sounds trivial, we need to state it: The reason that some games become cooperative if repeatedly played by the same players is that repeated cooperation creates trust that this cooperation will continue. This doesn’t even have to be a conscious process: Bacteria don’t ‘think’ why they do what they do. But the cooperative ones will thrive and multiply more, and eventually we end up with bacteria having ‘invented’ cooperation, or even co-evolution.

However, the spontaneous emergence of cooperation among repeat players does not occur where trust was never the problem to begin with.

In the stag hunt, we have an incentive to cooperate, if only we knew that the others will do the same. I have explained the reasons elsewhere in the context of the difficulty in negotiating climate change agreements.

In the prioner’s diemma, the situation is a little more tricky, in that we always have an incentive to defect, except when we know that we will face the same opponent again and again and he/she will recognize us. Then it pays to build trust that one will cooperate. (the “iterated prisoner’s dilemma”).

But the debt ceiling debate is a game of chicken: It is in my interest to cooperate only if I know the other person will not! Quoting from an earlier post:

Feigning madness can be a useful strategy in the game of “chicken” (also known as “brinkmanship” in the US): When the game is thus: head straight for the oncoming car of your opponent, and the loser is the one who swerves first, the rational strategy is to growl, scream, throw whisky bottles out the window, and generally appear as totally bereft of one’s senses.

The game of chicken makes you a ‘small loser’ if you walk away from the fight, but it makes you both very big losers if no-one gives in. Sounds familiar from the schoolyard? Well, exactly. Some games in life are set up that way.

Herein lies the problem: Appearing hell-bent on destroying the other is the right strategy in the game of chicken. The opponent will cooperate if he/she truly believes you will not. When you are in the schoolyard, before you walk away from the fight, lie about having knives, appear high on drugs, high on testosterone, already enraged…, whatever it takes to make the other think you might do anything! And if that doesn’t work, do the opposite and be reasonable; Be the ‘small’ loser. If the game is ‘Chicken’, that is the ‘right’ strategy which maximizes your ‘pay-off’.

Herein lies the much bigger problem: This only works once. At some point, you will have to ‘prove’ that you are mad.
Unlike ‘stag hunt’ or ‘prisoner’s dilemma’, ‘chicken’ gets harder and harder to play if you keep avoiding the disaster outcome repeatedly. Trust comes into the picture as a negative: I will not cooperate if I can trust you to cooperate, and I will definitely cooperate if I can rely on you being genuinely mad. And my assumption of what you will do will depend on what you have done in the past.

The entire political system in the US, from the constitution on up, was deliberately and rightly designed with lots of checks and balances, so that no-one can become too powerful and hi-jack government, in the sense of doing whatever one pleases. This works fantastically well if all sides act in good faith. However, the converse is also true: With lots of checks and balances anyone can hijack government in the sense of preventing it from doing what it wants or needs to do. The more we have checks and balances, the more we are at risk of being taken hostage by schoolyard bullies in the corridors of power calling us out into a game of chicken. Ironic, isn’t it? Aircraft safety engineering is familiar with that trend: There is a point beyond which more redundancy in the systems can increase the risk of failure. The more checks and balances you have, the more likely it is (a) on the positive side that you will catch a principal component failure early, but the more likely it is (b) on the negative side that a secondary component that was only there to create redundancy causes deadlock in the system which has become too interconnected.

There has to be a point then at which it is as mad to lend money to over-engineered government bureaucracies as it is to lend it to countries without the rule of law. In an over-engineered government apparatus, the right thing may not be allowed to happen, or not fast enough. You may not get your money back, for example, because someone in the government apparatus is playing chicken. In a country without the rule of law, the wrong thing can always happen at zero notice.

My guess is that the US is no-where near that point. But we will get there with absolute certainty, if the game of chicken gets repeated too often.

4 responses to “Game Theory and the Debt Ceiling

  1. Nice input on the checks and balances system in the U.S. being able to work in the way of hindering the branches from their goals as well as putting all of them on an equal footing.


  2. So, in the end they they had to sign an agreement. , for the Reps its like playing chicken with the other side driving a tank, and in that game you can feign madness as much as you want, you ‘re bound to lose!
    (Well, lets hope they are feigning !)


  3. Pingback: Varoufakis and Game Theory | The Sustainability Report·

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