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Hezbollah and the Prisoner's DilemmaCan game theory solve the Israel-Lebanon war?

By Tim Harford
Posted Thursday, Aug. 3, 2006, at 5:57 PM ET
Israeli armored forces operate against Hezbollah gunmen. Click image to expand.

Israel's strategy for dealing with Hezbollah has been called "tenfold deterrence": Any attack will be met with a far more forceful counterattack. Unfortunately both for Israelis and Lebanese, the strategy did not deter Hezbollah's missiles.

It might seem strange for an economist to offer even these obvious opinions on military strategy, but economists have been armchair generals since the development in the 1940s of game theory by John Von Neumann, a mathematician, and Oskar Morgenstern, an economist. Game theory is the study of situations in which each side's actions influence and are influenced by the other side's actions. Since the Second World War, game theorists have pondered strategy, deterrence, and Armageddon.

Game theory's power to summarize complex situations in a simple model is sometimes too seductive. The two most overinterpreted ideas in game theory are related to deterrence: the prisoner's dilemma and the strategy sometimes believed to "solve" the dilemma, "tit for tat."

The prisoner's dilemma was popularized by a simple story. Two men are captured by the police and separately offered the same plea-bargain: "If you confess and he doesn't, you walk free; if you both confess, you'll both get five years; if neither of you confess, you'll both get one year; if he confesses and you don't, you'll get 20 years." Rational prisoners will confess, wishing there was a way to commit each other to silence. Game theorists have known since the 1950s that when the prisoner's dilemma is repeated indefinitely, more cooperative strategies can flourish. This insight was independently rediscovered and made famous by Robert Axelrod, a political scientist who organized a computerized tournament in which competitors submitted simple programs to play the prisoner's dilemma. The champion was "tit for tat," which begins by cooperating with its fellow prisoner (staying silent) but punishes a squealer by confessing on the next turn. Axelrod argued that "tit for tat" was successful because it was easy to interpret, hard to exploit, began cooperatively, and quickly forgave transgressions by returning to cooperation. It has proved a magical myth: that you should speak softly and carry a big stick, that "an eye for an eye" can produce cooperation in unpromising situations. Axelrod's idea was repeated in a horde of popular science books.

But "tit for tat" is just a little too much of a poster child. The repeated prisoner's dilemma is a poor description of real-world situations. It didn't describe the Cold War, when a nuclear exchange was a one-off game if ever there was one. It doesn't describe the asymmetric struggle between Israel on one hand and multiple decision makers—Lebanon? Hezbollah?—on the other.

Most important, the "prisoner's dilemma" is merely a two-player game. Game theorists such as Ken Binmore, a professor at University College London, say this is a crucial omission. Most social arrangements stand or fail with the help of third parties. The crisis in Lebanon will be no exception.

In any case, "tit for tat" is not quite as successful as conventional wisdom would have you believe. A team from Southampton University kicked "tit for tat" off the top spot in a rerun of Axelrod's tournament by entering a collection of team players who colluded with each other. Another successful strategy is "tat for tit," which first tries to exploit the other person and plays nicely only if that doesn't work. Another winning approach is even more depressing, punishing cheats with eternal vengeance.

It is known simply as "grim."

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Tim Harford is a columnist for the Financial Times. He is the author of The Undercover Economist, and his latest book is The Logic of Life.
Photograph of Israeli armed forces in Lebanon by Uriel Sinai/Getty Images.
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