Convex Optimization, Game Theory, and Variational Inequality Theory

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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].”
Learning in games with continuous action sets and unknown payoff functions (2016, methodology): “the pure strategy level, several authors have considered VI-based and Gauss–Seidel methods for solving generalized Nash equilibrium problems (GNEPs); for a survey, see Facchinei and Kanzow (2007) and Scutari et al. (2010). The intersection of these works with the current paper is when the game satis”
Differentiable Game Mechanics (2019, background): “Convergence in two-player games was studied in Singh et al. (2000). WoLF (Win or Learn Fast) converges to Nash equilibria in two-player two-action games (Bowling and Veloso, 2002).”
Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems (2013, background): “Two recent tutorials on the subject are [15], [16], while recent contributions using the more general mathematical theory of Variational Inequalities [17] are [18]–[20].”
Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization (2011, neutral): “optimization and game theory [5], [22], [37].”