ZERO: Playing Mathematical Programming Games

TL;DR

ZERO is an open-source C++ library that integrates Mathematical Programming and Game Theory to model and solve Reciprocally Bilinear Games, enabling the analysis of multi-agent strategic interactions with complex constraints.

Contribution

The paper introduces ZERO, a modular software library that extends capabilities for modeling and computing Nash equilibria in RBGs with support for complex problem types.

Findings

Provides a comprehensive toolkit for RBGs

Supports integer non-convexities and bilevel problems

Includes a case study on a Knapsack Game

Abstract

We present ZERO, a modular and extensible C++ library interfacing Mathematical Programming and Game Theory. ZERO provides a comprehensive toolkit of modeling interfaces and algorithms for Reciprocally Bilinear Games (RBGs), i.e., simultaneous non-cooperative games where each player solves a mathematical program with a linear objective in the player's variable and bilinear in its opponents' variables. This class of games generalizes the classical problems of Operations Research to a multi-agent setting. ZERO modular structure gives users all the elementary ingredients to design new game-theoretic models and algorithms for RBGs, and find their Nash equilibria. The library provides additional extended support for integer non-convexities, linear bilevel problems, and linear equilibrium problems with equilibrium constraints. We provide an overview of the software's key components and showcase a Knapsack Game, i.e., a game where each player solves a binary knapsack problem. Aiming to boost practical methodological contributions at the interplay of Mathematical Programming and Game Theory, we release ZERO as open-source software. Source code, documentation and examples are available at www.getzero.one.