Bounding the Uncertainty of Graphical Games: The Complexity of Simple Requirements, Pareto and Strong Nash Equilibria
Gianluigi Greco, Francesco Scarcello
We investigate the complexity of bounding the uncertainty of graphical games, and we provide new insight into the intrinsic difficulty of computing Nash equilibria. In particular, we show that, if one adds very simple and natural additional requirements to a graphical game, the existence of Nash equilibria is no longer guaranteed, and computing an equilibrium is an intractable problem. Moreover, if stronger equilibrium conditions are required for the game, we get hardness results for the second level of the polynomial hierarchy. Our results offer a clear picture of the complexity of mixed Nash equilibria in graphical games, and answer some open research questions posed by Conitzer and Sandholm (2003).
PDF Link: /papers/05/p225-greco.pdf
AUTHOR = "Gianluigi Greco
and Francesco Scarcello",
TITLE = "Bounding the Uncertainty of Graphical Games: The Complexity of Simple Requirements, Pareto and Strong Nash Equilibria",
BOOKTITLE = "Proceedings of the Twenty-First Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-05)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2005",
PAGES = "225--232"