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Life, Death and Game Theory in South Africa

Stephen L. Carter is a Bloomberg View columnist. He is a professor of law at Yale University and was a clerk to U.S. Supreme Court Justice Thurgood Marshall. His novels include “The Emperor of Ocean Park” and “Back Channel,” and his nonfiction includes “Civility” and “Integrity.”
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When I teach my courses on the ethics of warfare, I like to tease the students with Nobel economics laureate Thomas Schelling's advice for winning a game of chicken. As you speed toward the other driver, says Schelling, toss the steering wheel out the car window, to persuade your opponent that you won't be the first to turn away. Your irrationality frightens him. He swerves first; you win.

What brings Schelling's suggestion to mind is the standoff between the South African government and the illegal gold miners trapped undergroundin an abandoned mine shaft in Benoni, not far from Johannesburg. The shaft has partly collapsed. Rescue services are at the scene, but, so far, the government has arrested any miners who make it to the surface. Those remaining underground insist they would rather die.

The threat to arrest men buried deep underground at first blush seems cruel. But the government is on the horns of a dilemma. The Department of Mineral Resources estimates annual losses from illegal mining at about $500 million. The trapped miners, moreover, are mostly illegal immigrants, a group that is hugely unpopular in South Africa. Mineral Resources Minister Susan Shabangu promised last fall that those caught mining illegally would be sent to prison rather than merely fined as in the old days.

This is where Schelling's idea comes into play. You win the game of chicken by persuading your opponent that you'd rather die than swerve. And although I don't wish to minimize the potential human tragedy in the mining dispute, the afficionado of game theory cannot help but be fascinated by this real-world test.

I've never seen the precise dynamics of the Benoni standoff in the literature, but game theorists have modeled close analogies. Consider, for example, the following analysis of prison hunger strikes offered by Oxford University sociologist Michael Biggs:

The government clearly prefers the absence of a hunger strike or surrender by the prisoner over making a concession or letting the prisoner die. The government's dilemma, if a hunger strike begins, is that concession and death are both negative outcomes. The prisoner clearly prefers avoiding a hunger strike over a hunger strike that ends in surrender, and clearly prefers winning a concession over ending with surrender.

Thus far, the preference rankings map perfectly onto what is happening in South Africa. The government can't just let them die -- at least two bodies have already been found -- but also can't let them go. But what about the preferences of the miners?

Biggs divides his protesting prisoners into three types: the bluffer, who "is willing to endure temporary starvation in order to gain a concession, but prefers surrender to death"; the sacrificial prisoner, who "prefers to surrender to no hunger strike, but prefers a concession to death"; and the resolute prisoner, who prefers death to surrender but would rather end the protest than die. He similarly divided governments into two types: the conciliatory, which would rather concede than allow the prisoners to die, and the intransigent, whose preferences are the other way around.

It isn't difficult to work out where the equilibrium solutions lie, but that's assuming full information. For example, if the government knows that the prisoner is bluffing and the prisoner knows that the government is intransigent, the prisoner will surrender. If on the other hand the government knows that the prisoner is sacrificial, and the government knows that the prisoner is resolute, the hunger strike will succeed.

The problem is that in the real world, neither side likely knows, at least at the start, what type the other is. Therefore, the parties must signal to each other. And the greater the cost of the signal -- so the theorists tell us -- the more reliably information is conveyed. That's why Schelling advises throwing the steering wheel from the car window.

Thus it makes perfect sense, despite the horror of onlookers, for the government to continue to arrest each miner who emerges. Whatever the government's fallback position, the point of the arrests is to signal to the miners its intransigence. Similarly, even if the miners are bluffing, the longer they stay in the mine and risk death, the stronger the signal that they are actually sacrificial, and willing to die.

How will this all turn out? Were this a hunger strike in a North Korean prison camp, we could predict that the government would remain intransigent and allow the prisoners to die. A dictatorship that relies on rule through fear might actually enhance its reputational capital by inverting what seems to most of us the obvious order of priorities.

By contrast, hunger strikes often succeed in democratic countries precisely because the government cannot afford the hit to its reputation that a long hunger strike often entails. This concern likely helps explain the largely unremarked recent decision by the Barack Obama administration tocease disclosing hunger strikes by prisoners at Guantanamo. What happens in secret can't hurt a government's reputation.

Nevertheless, as Biggs points out, even a democratic government can't simply give in every time those it targets with imprisonment threaten to die. It's tricky, but vital, to find the balance between conciliation and intransigence.

I suspect that the miners will surrender in the end. Risking death for the sake of gold feels less admirable than sacrificing for a noble cause. But this is just another way of saying that I think the miners are bluffing. So far, the South African government is making the same bet. If the bet turns out to be wrong, the result will be catastrophic.

(Stephen L. Carter is a Bloomberg View columnist and a professor of law at Yale University. He is the author of "The Violence of Peace: America's Wars in the Age of Obama" and the novel "The Impeachment of Abraham Lincoln." Follow him on Twitter at @StepCarter.)

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