Theoretical models have struggled to make sharp predictions of which governments form in parliamentary systems and how long these governments last. We develop an AI algorithm to solve an analytically intractable coalition bargaining game. While AI models have penetrated most aspects of daily life, they have largely been ignored by political scientists. Formidable successes by AI models in solving games like Chess, Go, and especially a bluffing game like Poker, suggest they also have the potential to attack difficult political games.