NashOpt - A Python Library for Computing Generalized Nash Equilibria

TL;DR

NashOpt is an open-source Python library that efficiently computes generalized Nash equilibria in complex noncooperative games, supporting nonlinear, linear-quadratic, inverse, and Stackelberg game formulations with practical control applications.

Contribution

It introduces a unified framework leveraging KKT conditions and JAX for automatic differentiation to solve diverse GNE problems efficiently.

Findings

Successfully computes multiple equilibria in various game settings.

Demonstrates applications in control problems like LQR and MPC.

Provides an accessible tool for game-theoretic analysis and design.

Abstract

NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables. The library exploits the joint Karush-Kuhn-Tucker (KKT) conditions of all players to handle both general nonlinear GNEs and linear-quadratic games, including their variational versions. Nonlinear games are solved via nonlinear least-squares formulations, relying on JAX for automatic differentiation. Linear-quadratic GNEs are reformulated as mixed-integer linear programs, enabling efficient computation of multiple equilibria. The framework also supports inverse-game and Stackelberg game-design problems. The capabilities of NashOpt are demonstrated through several examples, including noncooperative game-theoretic control problems of linear quadratic regulation and model predictive control. The library is available at https://github.com/bemporad/nashopt