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Math Trek

Mathematical Fortune-Telling

How well can game theory solve business and political disputes?

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Predicting the future is not very hard, according to Bruce Bueno de Mesquita: a little mathematics is all you need. Figuring out how to manipulate a situation to achieve specific aims is a bit less straightforward, but Bueno de Mesquita says his mathematical tools can usually do that, too.

The New York University political science professor has developed a computerized game theory model that predicts the future of many business and political negotiations and also figures out ways to influence the outcome. Two independent evaluations, one by academics and one by the U.S. Central Intelligence Agency, have both shown that about 90 percent of his predictions have been accurate. Most recently, he has used his mathematical tools to offer approaches for handling the growing nuclear crisis with Iran.

Bueno de Mesquita provides the computer tools, but he relies on political or business experts to identify specific issues, their possible outcomes, and the key players. He asks experts narrow, carefully delineated questions about which outcome each player would prefer, how important the issue is to each player, and how much influence each player can exert. But he does not ask about the history of the conflict, the cultural norms of the area, or what the experts think will happen.

With careful interviewing, Bueno de Mesquita finds that he can get experts to agree on what information the model needs as input, even when the experts disagree sharply on expected outcomes. Once, after generating a report for the CIA using information from the agency's experts, he had his students assemble the same information from news reports. "Over 90 percent of them came up with the same results as I got [when I was] locked in a lead-lined vault at the CIA headquarters," Bueno de Mesquita says. "It's basic information that experts agree on and that you can even find in The Economist."

The elements of the model are players standing in for the real-life people who influence a negotiation or decision. At each round of the game, players make proposals to one or more of the other players and reject or accept proposals made to them. Through this process, the players learn about one another and adapt their future proposals accordingly. Each player incurs a small cost for making a proposal. Once the accepted proposals are good enough that no player is willing to go to the trouble to make another proposal, the game ends. The accepted proposals are the predicted outcome.

To accommodate the vagaries of human nature, the players are cursed with divided souls. Although all the players want to get their own preferred policies adopted, they also want personal glory. Some players are policy-wonks who care only a little about glory, while others resemble egomaniacs for whom policies are secondary. Only the players themselves know how much they care about each of those goals. An important aspect of the negotiation process is that by seeing which proposals are accepted or rejected, players are able to figure out more about how much other players care about getting their preferred policy or getting the glory.

The details of his study of negotiation options with Iran are classified, but Bueno de Mesquita says that the broad outline is that there is nothing the United States can do to prevent Iran from pursuing nuclear energy for civilian power generation. The more aggressively the U.S. responds to Iran, he says, the more likely it is that Iran will develop nuclear weapons. The upshot of the study, Bueno de Mesquita argues, is that the international community needs to find out if there is a way to monitor civilian nuclear energy projects in Iran thoroughly enough to ensure that Iran is not developing weapons.

One of his most famous past predictions also concerned Iran. In 1984, the model predicted that when Ayatollah Khomeini died, an ayatollah named Hojatolislam Khameini and a little-known cleric named Hasheimi Rafsanjani would rise to succeed Khomeini as leaders of Iran. At the time, most experts considered that outcome exceedingly unlikely, since Khomeini had designated a different person as his successor. But in fact, when Khomeini died five years later, Rafsanjani and Khameini succeeded him.

Bueno de Mesquita says he also predicted that Andropov would succeed Brezhnev long before experts considered it likely. He foresaw that China would reclaim Hong Kong 12 years before it happened, and he predicted that France would narrowly pass the European Union's Maastricht Treaty.

Former CIA analyst Stanley Feder says that he has used Bueno de Mesquita's model well over a thousand times since the early 1980s to make predictions about specific policies. Like others, he has found it to be more than 90 percent accurate. In situations where predictions of the model differed from experts' predictions, the model always turned out to be correct.

"I'm always stunned that it works so well," Bueno de Mesquita says. "This 90 percent is not my assessment."

The main reason that the model generates more reliable predictions than experts do is that "the computer doesn't get bored, it doesn't get tired, and it doesn't forget," he says. In the analysis of nuclear technology development in Iran, for example, experts identified 80 relevant players. Because no individual can keep track of all the possible interactions between so many players, human analysts focus on five or six key players. The lesser players may not have a lot of power, Buena de Mesquita says, but they tend to be knowledgeable enough to influence how key decision-makers understand the issues. His model can keep track of those influences when a human can't.

"Given expert input of data for the variables for such a model, it would not surprise me in the least to see that it would perform well," says Branislav L. Slantchev, a political scientist and game theorist at the University of California at San Diego. Predictions based on game theory can fail in a context where people don't act rationally, but in Buena de Mesquita's work, Slantchev says, rational action mostly means that the players are promoting their own perceived interests as best they can, something humans tend to do.

However, he points out that the model relies on having a considerable amount of expert input. "Honestly, if you had all this information," Slantchev says, "you should be able to predict fairly well how the issue would be resolved." The main reason that the model does this better than experts is that it "strips ideological blindfolds, cultural prejudice, and normative commitments that very often color the view of experts."

Buena de Mesquita offers his services through Mesquita and Roundell, a company he founded that uses his model to advise businesses and governments. "It's pretty exciting when you sit down with a client," he says, "and you know that they're making decisions involving life and death questions or billions of dollars, and at the end of the day they are relying on a body of equations."


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