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There has been significant recent interest in computing effective strategies for playing large imperfect-information games. Much prior work involves computing an approximate equilibrium strategy in a smaller abstract game, then playing this strategy in the full game (with the hope that it also well approximates an equilibrium in the full game). In this… (More)

Computing a Nash equilibrium in multiplayer stochastic games is a notoriously difficult problem. Prior algorithms have been proven to converge in extremely limited settings and have only been tested on small problems. In contrast, we recently presented an algorithm for computing approximate jam/fold equilibrium strategies in a three-player no-limit Texas… (More)

We develop an algorithm for opponent modeling in large extensive-form games of imperfect information. It works by observing the opponent's action frequencies and building an opponent model by combining information from a precom-puted equilibrium strategy with the observations. It then computes and plays a best response to this opponent model; the opponent… (More)

A recent paper computes near-optimal strategies for two-player no-limit Texas hold'em tournaments; however, the techniques used are unable to compute equilibrium strategies for tournaments with more than two players. Motivated by the widespread popularity of multiplayer tournaments and the observation that jam/fold strategies are near-optimal in the two… (More)

The leading approach for solving large imperfect-information games is automated abstraction followed by running an equilibrium finding algorithm. We introduce a distributed version of the most commonly used equilibrium-finding algorithm , counterfactual regret minimization (CFR), which enables CFR to scale to dramatically larger abstractions and numbers of… (More)

When solving extensive-form games with large action spaces, typically significant abstraction is needed to make the problem manageable from a modeling or computational perspective. When this occurs, a procedure is needed to interpret actions of the opponent that fall outside of our abstraction (by mapping them to actions in our abstraction). This is called… (More)

There is often a large disparity between the size of a game we wish to solve and the size of the largest instances solv-able by the best algorithms; for example, a popular variant of poker has about 10 165 nodes in its game tree, while the currently best approximate equilibrium-finding algorithms scale to games with around 10 12 nodes. In order to… (More)

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We also acknowledge Intel Corporation and IBM for their machine gifts. Abstract We present a new approach for solving large (even infinite) multiplayer games of… (More)

We consider the problem of playing a finitely-repeated two-player zero-sum game safely---that is, guaranteeing at least the value of the game per period in expectation regardless of the strategy used by the opponent. Playing a stage-game equilibrium strategy at each time step clearly guarantees safety, and prior work has conjectured that it is impossible to… (More)

Sequential games of perfect information can be solved by backward induction, where solutions to endgames are propagated up the game tree. However, this does not work in imperfect-information games because different endgames can contain states that belong to the same information set and cannot be treated independently. In fact, we show that this approach can… (More)