Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Computing Nash equilibria of action-graph games
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A polynomial-time algorithm for action-graph games
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Fast and compact: a simple class of congestion games
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Symmetries and the complexity of pure Nash equilibrium
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the complexity of Nash equilibria of action-graph games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
On the complexity of nash dynamics and sink equilibria
Proceedings of the 10th ACM conference on Electronic commerce
Computing pure strategy nash equilibria in compact symmetric games
Proceedings of the 11th ACM conference on Electronic commerce
Decentralized MDPs with sparse interactions
Artificial Intelligence
Rational Generating Functions and Integer Programming Games
Operations Research
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We analyze the problem of computing pure Nash equilibria in action graph games (AGGs), which are a compact game-theoretic representation. While the problem is NP-complete in general, for certain classes of AGGs there exist polynomial time algorithms. We propose a dynamic-programming approach that constructs equilibria of the game from equilibria of restricted games played on subgraphs of the action graph. In particular, if the game is symmetric and the action graph has bounded treewidth, our algorithm determines the existence of pure Nash equilibrium in polynomial time.