## Can Game Theory Predict When Iran Will Get the Bomb?

Wednesday, August 19th, 2009

Bruce Bueno de Mesquita has a new book coming out for a popular audience, The Predictioneer’s Game, and Clive Thompson of the New York Times visits him to ask, Can game theory predict when Iran will get the Bomb?

A tall man with a slab of gray hair, Bueno de Mesquita, who is 62, welcomed me with painstakingly prepared cups of espresso. Then he pulled out his beat-up I.B.M. laptop — so old that the lettering on the A, S, D and E keys was worn off — and showed me a spreadsheet that summarized Iran’s future.

The spreadsheet included almost 90 players. Some were people, like the Iranian president, Mahmoud Ahmadinejad, and Supreme Leader Ali Khamenei; others were groups, like the U.N. Security Council and Iran’s “religious radicals.” Next to each player, a number represented one variable in Bueno de Mesquita’s model: the extent to which a player wanted Iran to have the ability to make nuclear weapons. The scale went from 0 to 200, with 0 being “no nuclear capacity at all” and 200 representing a test of a nuclear missile.

At the beginning of the simulation, the positions were what you would expect. The United States and Israel and most of Europe wanted Iran to have virtually no nuclear capacity, so their preferred outcomes were close to zero. In contrast, the Iranian hard-liners were aggressive. “This is not only ‘Build a bomb,’ ” Bueno de Mesquita said, characterizing their position. “It’s probably: ‘We should test a bomb.’ ”

But as the computer model ran forward in time, through 2009 and into 2010, positions shifted. American and Israeli national-security players grudgingly accepted that they could tolerate Iran having some civilian nuclear-energy capacity. Ahmadinejad, Khamenei and the religious radicals wavered; then, as the model reached our present day, their power — another variable in Bueno de Mesquita’s model — sagged significantly.

Amid the thousands of rows on the spreadsheet, there’s one called Forecast. It consists of a single number that represents the most likely consensus of all the players. It begins at 160 — bomb-making territory — but by next year settles at 118, where it doesn’t move much. “That’s the outcome,” Bueno de Mesquita said confidently, tapping the screen.

What does 118 mean? It means that Iran won’t make a nuclear bomb. By early 2010, according to the forecast, Iran will be at the brink of developing one, but then it will stop and go no further. If this computer model is right, all the dire portents we’ve seen in recent months — the brutal crackdown on protesters, the dubious confessions, Khamenei’s accusations of American subterfuge — are masking a tectonic shift. The moderates are winning, even if we cannot see that yet.

Bueno de Mesquita’s model is loosely based on Duncan Black’s analysis of committee voting:

To predict how leaders will behave in a conflict, Bueno de Mesquita starts with a specific prediction he wants to make, then interviews four or five experts who know the situation well. He identifies the stakeholders who will exert pressure on the outcome (typically 20 or 30 players) and gets the experts to assign values to the stakeholders in four categories: What outcome do the players want? How hard will they work to get it? How much clout can they exert on others? How firm is their resolve? Each value is expressed as a number on its own arbitrary scale, like 0 to 200. (Sometimes Bueno de Mesquita skips the experts, simply reads newspaper and journal articles and generates his own list of players and numbers.) For example, in the case of Iran’s bomb, Bueno de Mesquita set Ahmadinejad’s preferred outcome at 180 and, on a scale of 0 to 100, his desire to get it at 90, his power at 5 and his resolve at 90.

Then the math begins, some of which is surprisingly simple. If you merely sort the players according to how badly they want a bomb and how much support they have among others, you will end up with a reasonably good prediction. But the other variables enable the computer model to perform much more complicated assessments. In essence, it looks for possible groupings of players who would be willing to shift their positions toward one another if they thought that doing so would be to their advantage. The model begins by working out the average position of all the players — the “middle ground” that exerts a gravitational force on the whole negotiation. Then it compares each player with every other player, estimating whether one will be able to persuade or coerce the others to move toward its position, based on the power, resolve and positioning of everyone else. (Power isn’t everything. If the most powerful player is on the fringe of an issue, and a cluster of less-powerful players are closer to the middle, they might exert greater influence.) After estimating how much or how little each player might budge, the software recalculates the middle ground, which shifts as the players move. A “round” is over; the software repeats the process, round after round. The game ends when players no longer move very much from round to round — this indicates they have compromised as much as they ever will. At that point, assuming no player with veto power had refused to compromise, the final average middle-ground position of all the players is the result — the official prediction of how the issue will resolve itself.

The computer model, in short, predicts coalitions.