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Extensive games are a powerful model of multiagent decision-making scenarios with incomplete information. Finding a Nash equilibrium for very large instances of these games has received a great deal of recent attention. In this paper, we describe a new technique for solving large games based on regret minimization. In particular, we introduce the notion of(More)
Perfect recall is the common and natural assumption that an agent never forgets. As a consequence, the agent can always condition its choice of action on any prior observations. In this paper, we explore relaxing this assumption. We observe the negative impact this relaxation has on algorithms: some algorithms are no longer well-defined, while others lose(More)
Extensive-form games are a powerful model for representing interactions between agents. Nash equilibrium strategies are a common solution concept for extensive-form games and, in two-player zero-sum games, there are efficient algorithms for calculating such strategies. In large games, this computation may require too much memory and time to be tractable. A(More)
Decomposition, i.e., independently analyzing possible sub-games, has proven to be an essential principle for effective decision-making in perfect information games. However, in imperfect information games, decomposition has proven to be problematic. To date, all proposed techniques for decomposition in imperfect information games have abandoned theoretical(More)
Recently, there has been considerable progress towards algorithms for approximating Nash equilibrium strategies in extensive games. One such algorithm, Counterfactual Regret Minimization (CFR), has proven to be effective in two-player zero-sum poker domains. While the basic algorithm is iterative and performs a full game traversal on each iteration,(More)
Adaptation to other initially unknown agents often requires computing an effective counter-strategy. In the Bayesian paradigm, one must find a good counter-strategy to the inferred posterior of the other agents' behavior. In the experts paradigm, one may want to choose experts that are good counter-strategies to the other agents' expected behavior. In this(More)
One fundamental evaluation criteria of an AI technique is its performance in the worst-case. For static strategies in extensive games, this can be computed using a best response computation. Conventionally , this requires a full game tree traver-sal. For very large games, such as poker, that traversal is infeasible to perform on modern hardware. In this(More)
In 1981 Claude Berge asked about combinatorial properties that might be used to solve Hex puzzles. In response, we establish properties of dead, or negligible, cells in Hex and the Shannon game. A cell is dead if the colour of any stone placed there is irrelevant to the theoretical outcome of the game. We show that dead cell recognition is NP-complete for(More)