Automatically generating abstractions for planning
Artificial Intelligence
On state-space abstraction for anytime evaluation of Bayesian networks
ACM SIGART Bulletin
Representations and solutions for game-theoretic problems
Artificial Intelligence - Special issue on economic principles of multi-agent systems
Primal-dual interior-point methods
Primal-dual interior-point methods
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Artificial Intelligence - Chips challenging champions: games, computers and Artificial Intelligence
Introduction to Algorithms
GIB: Steps Toward an Expert-Level Bridge-Playing Program
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Computing approximate bayes-nash equilibria in tree-games of incomplete information
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash equilibria of action-graph games
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing sequential equilibria for two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Sequences of take-it-or-leave-it offers: near-optimal auctions without full valuation revelation
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Simple search methods for finding a Nash equilibrium
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Optimal Rhode Island Hold'em poker
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 4
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Approximating game-theoretic optimal strategies for full-scale poker
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A continuation method for Nash equilibria in structured games
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Gradient-based algorithms for finding Nash equilibria in extensive form games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Fast algorithms for finding proper strategies in game trees
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Computing an approximate jam/fold equilibrium for 3-player no-limit Texas Hold'em tournaments
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems: demo papers
Effective short-term opponent exploitation in simplified poker
Machine Learning
Computing an Extensive-Form Correlated Equilibrium in Polynomial Time
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Gradient-based algorithms for finding Nash equilibria in extensive form games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Artificial Intelligence
Lossy stochastic game abstraction with bounds
Proceedings of the 13th ACM Conference on Electronic Commerce
New results on the verification of Nash refinements for extensive-form games
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Strategy purification and thresholding: effective non-equilibrium approaches for playing large games
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Bilateral bargaining with one-sided uncertain reserve prices
Autonomous Agents and Multi-Agent Systems
A parameterized family of equilibrium profiles for three-player kuhn poker
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Evaluating state-space abstractions in extensive-form games
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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Finding an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomorphic abstraction transformation. For a multi-player sequential game of imperfect information with observable actions and an ordered signal space, we prove that any Nash equilibrium in an abstracted smaller game, obtained by one or more applications of the transformation, can be easily converted into a Nash equilibrium in the original game. We present an algorithm, GameShrink, for abstracting the game using our isomorphism exhaustively. Its complexity is õ(n2), where n is the number of nodes in a structure we call the signal tree. It is no larger than the game tree, and on nontrivial games it is drastically smaller, so GameShrink has time and space complexity sublinear in the size of the game tree. Using GameShrink, we find an equilibrium to a poker game with 3.1 billion nodes—over four orders of magnitude more than in the largest poker game solved previously. To address even larger games, we introduce approximation methods that do not preserve equilibrium, but nevertheless yield (ex post) provably close-to-optimal strategies.