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I recall hearing a story about the use of game theory in the US to predict how power would shift between top members of the government. In this case the predictions were initially disregarded since it didn't appear conceivable that the person they said would end up in power could gain power due to him being too minor, however it turned out that this person gained power to the surprise of everyone. This person then later lost power and tried to hire the game theorist who made those predictions to tell them what they needed to do to regain power. In this case the game theorist ignored them and contacted the CIA about this incident.

Unfortunately I can't find anything with these vague details online and was hoping that this story would be familiar to people on this stack exchange. Further details are that I believe the government in question was in the middle east and I know it was not a democracy (since only a small number of actors needed to be considered and so could be approached with game theory).

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Given the details, I'm pretty sure you're referring to Bruce Bueno de Mesquita. He predicted that Ali Khamenei would succeed Ruhollah Khomeini as Supreme Leader of Iran in 1984, five years before the latter's death, and further predicted that Akbar Hashemi Rafsanjani would take over from Khamenei. This has not happened as of yet.

One of his other various successes includes predicting that President Pervez Musharraf of Pakistan would leave office in 2008, accurate to within a month. He has also worked with the CIA.

He was covered in detail by the New York Times in 2009, and by the Economist in 2011.

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