On Operator Theory and Applications in Game Theory

This article presents an overview of operator theory, operator-splitting methods, and their applications. It shows that many existing algorithms in optimization and games can be abstracted to an operator-theoretic problem that often requires only minimal conditions. The main advantage is that an operator-theoretic approach is unifying and can simplify complicated convergence proofs. The article reviews some of the applications of this approach, with a focus on game-theoretic algorithms.