We develop and evaluate a new exact algorithm for finding Nash equilibria of two-player zero-sum extensive-form games with imperfect information. Our approach is based on the sequence-form representation of the game, and uses an algorithmic framework of double-oracle methods that have been used successfully in other classes of games. The algorithm uses an iterative decomposition, solving restricted games and exploiting fast best-response algorithms to add additional sequences to the game over time. We demonstrate our algorithm on a class of adversarial graph search games motivated by real world border patrolling scenarios. The results indicate that our framework is a promising way to scale up solutions for extensive-form games, reducing both memory and computation time requirements.
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