ZERO: Playing Mathematical Programming Games

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.