Monotone Operator Methods for Nash Equilibria in Non-potential Games

By Luis M. Briceño-Arias, Patrick L. Combettes. 2011

76 citations recorded by the source corpus.

We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximation problems are demonstrated.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/49a1691924a52cb656d5695fdc5968041ebbed04

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Citations in the corpus

Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators (2015, background): “1 are found in areas such as evolution inclusions [2], Nash equilibria [7], image recovery [8, 10, 16], inverse problems [9, 13], signal processing [21], statistics [25], machine learning [26], variational inequalities”
A splitting algorithm for dual monotone inclusions involving cocoercive operators (2011, background): “, evolution inclusions [3], partial differential equations [2, 20, 23], mechanics [21], variational inequalities [6, 19], Nash equilibria [8], and various optimization problems [7, 9, 10, 14, 16, 17, 25, 29].”
Variable metric forward–backward splitting with applications to monotone inclusions in duality (2012, background): “This framework is quite central due to the large class of problems it encompasses in areas such as partial differential equations, mechanics, evolution inclusions, signal and image processing, best approximation, convex optimization, learning theory, inverse problems, statistics, game theory and var”