# A study on the stability and efficiency of graphical games with unbounded treewidth

1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
2 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
3 SMA - Systèmes Multi-Agents
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : 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 ($\epsilon$-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.
Document type :
Conference papers

Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-01216035
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IsmailiEtALAAMAS2013.pdf
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• HAL Id : hal-01216035, version 1

### Citation

Anisse Ismaili, Evripidis Bampis, Nicolas Maudet, Patrice Perny. A study on the stability and efficiency of graphical games with unbounded treewidth. 12th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2013), May 2013, Saint Paul, MN, United States. pp.263-270. ⟨hal-01216035⟩

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