Nash Equilibrium Problems with Descent Information

• Grant number: 25/00034-0
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2025
• End date: February 28, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Roberto Andreani
• Grantee: Piero Andreeto Liduvino Ribeiro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/08706-1 - Numerical optimization, AP.TEM

Abstract

This project aims to study methods for solving Nash Equilibrium Problems (NEPs) that aggregate descent information throughout the iterative process. In a recent paper by the group, the authors identified that Newton's method for the first-order conditions of an unconstrained NEP can be interpreted as a strategy for the best response of players to a decision predicted for the other player. Initially, we hope to delve deeper into this algorithm, seeking to obtain better convergence results and relate it to other descent strategies based on reformulations of the problem, such as the Nikaido Isoda function, and dynamic learning techniques. In a subsequent step, we intend to generalize the method to NEPs with box constraints and then to nonlinear constraints. The project should contemplate both theoretical aspects and efficient implementations of algorithms for numerical tests in relevant applications.