Generalized Nash equilibrium problems

By Francisco Facchinei, Christian Kanzow. 2007

1,378 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Numerical Analysis, Mathematical Optimization, Game & Decision Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Economics and Econometrics

In Numerical Analysis

In Mathematical Optimization

In Game & Decision Theory

Citations in the corpus

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity (2021, background): “Problem (1) generalizes the solution of several types of stochastic smooth games [Facchinei and Kanzow, 2007, Scutari et al., 2010, Mertikopoulos and Zhou, 2019].”
Convex Optimization, Game Theory, and Variational Inequality Theory (2010, background): “A survey on GNEPs, with much historical information, is given in [23].”
Differentiable Game Mechanics (2019, background): “Convergence has also been studied in various n -player settings, see Rosen (1965); Scutari et al. (2010); Facchinei and Kanzow (2010); Mertikopoulos and Zhou (2016).”
Convex Optimization in Signal Processing and Communications (2009, neutral): “6 The figure on the left shows the convergence behavior of the constraint violation for the two primal sequences, {x k } and {ˆx k }.”
BM3D Frames and Variational Image Deblurring (2011, background): “In terms of the game theory, problem (34) can be interpreted as a game of two players identified, respectively, with two variables and [19], [20].”
Learning in games with continuous action sets and unknown payoff functions (2016, neutral): “Otherwise, with regard to pure-action learning in concave games, several authors have considered VI-based approaches, Gauss–Seidel best-response schemes, and Nikaido–Isoda relaxation meth-ods for solving generalized Nash equilibrium problems; for a survey, see Facchinei and Kanzow [11] and Scutari e”
Distributed Nash equilibrium seeking for aggregative games with coupled constraints (2016, background): “Lemma 4 (Facchinei & Kanzow 2010, Theorem 3.9) If K is convex, every solution of the VI(K, F ) is also a GNE.”
Stable Opponent Shaping in Differentiable Games (2018, background): “Convergence has widely been studied in convex n -player games, see especially Rosen (1965); Facchinei & Kanzow (2007).”
On the convergence of single-call stochastic extra-gradient methods (2019, background): “As for saddle-point problems and smooth games, variants of this condition can be found in several different sources, see e.g., [16, 24, 29, 40, 41] and references therein.”
Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants (2014, neutral): “tandard deviation , where = 0:025. We note that Aand vare also generated randomly as stated earlier. The resulting game is a shared constraint Nash game and a (variational) equilibrium of this game [59] is given by a variational inequality problem. Note that agent payos are pseudoconcave [34, Theore”
Equilibria in an Oligopolistic Electricity Pool With Stepwise Offer Curves (2012, background): “However, it is well known [2] that this type of GNEP may have no solutions, multiple solutions, or infinitely many solutions.”