[show abstract][hide abstract] ABSTRACT: We develop a polynomial-time algorithm for finding correlated equilibria (a well-studied notion of rationality due to Aumann that generalizes the Nash equilibrium) in a broad class of succinctly representable multiplayer games, encompassing essentially all known kinds, including all graphical games, polymatrix games, congestion games, scheduling games, local effect games, as well as several generalizations. Our algorithm is based on a variant of the existence proof due to Hart and Schmeidler , and employs linear programming duality, the ellipsoid algorithm, Markov chain steady state computations, as well as application-specific methods for computing multivariate expectations.
Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 22-24, 2005; 01/2005
[show abstract][hide abstract] ABSTRACT: We discuss sensitivity of equilibrium points in bimatrix games depending on small variances (perturbations) of data. Applying
implicit function theorem to a linear complementarity problem which is equivalent to the bimatrix game, we investigate sensitivity
of equilibrium points with respect to the perturbation of parameters in the game. Namely, we provide the calculation of equilibrium
points derivatives with respect to the parameters.
Journal of Applied Mathematics and Computing 05/1996; 3(2):149-156.
[show abstract][hide abstract] ABSTRACT: We investigate from the computational viewpoint multi-player games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the sym- metric network case, while the problem is PLS-complete in general. We discuss implications to non-atomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.
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