On the Equilibria Computation of Set-Valued Lur'e Dynamical Systems

TL;DR

This paper introduces an efficient method for computing equilibria in set-valued Lur'e dynamical systems, which are crucial for system analysis and solving related quasi-variational inequalities, including applications in game theory.

Contribution

It presents a novel computational approach for equilibria in set-valued Lur'e systems, extending to quasi-variational inequalities and Nash equilibrium problems.

Findings

Efficient equilibrium computation method for set-valued Lur'e systems

Application to solving quasi-variational inequalities

Examples demonstrating Nash quasi-equilibria in game theory

Abstract

In this article, we propose an efficient way to compute equilibria of a general class of set-valued Lur'e dynamical systems, which plays an important role in the asymptotical analysis of the systems. Besides the equilibria computation, our study can be also used to solve a class of quasi-variational inequalities. Some examples of finding Nash quasi-equilibria in game theory are given.