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).