Nonserial Dynamic Programming
Multi-agent algorithms for solving graphical games
Eighteenth national conference on Artificial intelligence
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Constraint satisfaction algorithms for graphical games
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
The impact of network topology on pure Nash equilibria in graphical games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Pure Nash equilibria: complete characterization of hard and easy graphical games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
libDAI: A Free and Open Source C++ Library for Discrete Approximate Inference in Graphical Models
The Journal of Machine Learning Research
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Treewidth of Erdős-Rényi random graphs, random intersection graphs, and scale-free random graphs
Discrete Applied Mathematics
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Graphical games (GG) provide compact representations of multiplayer games involving large populations of agents when influences among them have some locality property. The notion of pure Nash equilibrium (PNE), not requiring randomized strategies, is a fundamental stability concept. However, recent results show that for many natural topologies, a PNE is very unlikely to exist when the number of agents is large, which challenges the relevance of PNE in large GG. In this paper, we investigate how far we can get from the notion of individual stability captured by the concept of PNE, by only requiring agents to be almost in best-response (ε-Nash), or by requiring almost all agents to be in best-response. We study these approximated notions of PNE for different topologies, including graphs with unbounded treewidth, like grids. This makes the problem computationnally very challenging and requires the comparison and use of several algorithmic solutions. Our results reveal surprisingly good asymptotic properties, tempering the claim that individual stability is not a relevant notion for large GG. Finally, as approximated PNE provide various tradeoffs between stability and social utility maximization, we propose an approach to construct a minimal-size $e$-covering of all feasible Pareto-dominant tradeoffs.