Game dynamics – Optimization Online

A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

Published: 2024/03/07

Game Theory, Nonlinear Optimization, Other Topics Game dynamics, Jacobi-type methods, nash equilibrium, Newtonian method, Non-convex game

A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering they are taking their current … Read more

A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

Published: 2022/09/22, Updated: 2023/05/26

Luís Felipe Bueno

Gabriel Haeser

Oliver Kolossoski

Game Theory, Other Topics Game dynamics, game theory, Jacobi-type methods, nash equilibrium, Newtonian method, Non-convex games

A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering that they … Read more