Monday 17 July 2017

On Schell, Schelling, and Nuclear War

As a mathematical tool, game theory is useful for formalizing our intuitions so we can analyze them systematically. Game theory is most powerful, however, when it shows us that rigorous thinking can lead to counter-intuitive results. In this post I juxtapose two writers—Jonathan Schell, a journalist, and Thomas Schelling, a game theorist—who have thought in incredible depth about one of the gravest threats to mankind’s existence: the possibility of nuclear war.

I first learned about Jonathan Schell by reading his obituary in March 2014.1 Schell authored ‘The Fate of the Earth’ which is, at once, a visceral, historical account of the atomic bombing of Hiroshima and a scientific and philosophical meditation on the possibility of human extinction by nuclear war. The book draws its power by opening with actual accounts of the horrifying effects of an atomic weapon—the fire spread through the city, outpacing its fleeing populace, masses more dying of radiation sickness—then shifting fluidly to hypotheticals in which New York City is attacked with a nuclear weapon. It discusses the predicted sky-scorching effects of all-out nuclear war and dwells on the bleak prospect of a extinction, of an infinite future in which humans are absent from the Universe. Schell’s position—his conclusion—was that the only way to prevent nuclear holocaust was a worldwide movement of nuclear disarmament. As long as nuclear weapons are in existence, the risk of them being used, however infinitesimal, is too high.

If we agree that complete disarmament is a desirable end point (a hotly debated topic), can we actually get there in practice? This is where Schelling comes in. Schelling is known within social science for breakthrough contributions to the analysis of coordination, a thorny corner of game theory where the standard Nash Equilibrium solution concept gives rise to a proliferation of equilibria, and for pioneering the use of computational models to show that small shifts in individual-level preferences can cause large changes in society-scale outcomes.2

The interplay of game theory as a scholarly field and nuclear strategy as a matter of applied international relations goes back a long way. The concept of ‘mutually assured destruction,’ often going by the acronym, MAD, is a game-theoretic one. It basically says neither adversary in a nuclear conflict will employ a first-strike strategy if it knows that the other side will retain the capability to wipe it out through retaliation. The doctrine of has MAD entered the popular discourse, and was parodied perfectly by Kubrick’s Dr. Strangelove.

An interesting—and very practical—corollary of MAD reasoning is explored by Schelling in the Appendix to his 1960 classic ‘The Strategy of Conflict.’ He argues, and shows mathematically, that partial nuclear disarmament is extremely risky. The capability to wipe out an opponent even after one has suffered a pre-emptive strike is what lends the mutually assured destruction set-up its stability. An opponent who fears they will have no capability left with which to retaliate if they are attacked has greater reason to take the risk of initiating the first strike. The upshot of the game-theoretic analysis is the rather counter-intuitive result that partial disarmament is worse than no disarmament at all.

The von Neumann / Schelling / MAD reasoning was based on the Cold War context which basically entailed two largely-symmetric, competing nuclear powers. Game theory also assumes actors behave ‘rationally,’ i.e. each actor is self-interested and forward-looking and assumes that other actors are too. This seems to have been a reasonable assumption for that era.3 As of 2017 it is not clear these same assumptions apply, which is a cause for concern. The ‘players’ in today’s nuclear ‘game’ are not so symmetric, nor is it clear that they will behave as predictably as economists’ rational actors do. It seems that it is for this reason that the Bulletin of the Atomic Scientists has moved its Doomsday Clock to ‘two and a half minutes to midnight,’ its riskiest point since 1953. It is a wise time to revisit the writings of both Schell and Schelling, take seriously this existential threat, and hope that cool heads will prevail.

1 Another post on this blog that was first inspired by an obituary is the one discussing the work of James Martin, who passed away in 2013. The following summer I read both Schell’s and Martin’s landmark books. Some of my thoughts on Martin’s ‘The Meaning of the 21st Century’ are recorded here.
2 An excellent analysis of the organizational apparatus underlying the military strategy during the Cuban missile crisis is provided by Graham Allison in his classic, ‘Essence of Decision.’
3 Other posts I've written drawing on Schelling's ideas can be found here and here.