We present ZERO, a modular and extensible C++ library interfacing Mathematical Programming and Game Theory. ZERO provides a comprehensive toolkit of modeling interfaces for designing games, helper tools, and algorithms to find Nash equilibria. Specifically, the software supports 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 to a multi-agent setting the classical problems of Operations Research. ZERO provides extended support for integer non-convexities, linear bilevel problems, and linear equilibrium problems with equilibrium constraints. Its modular structure provides users with all the elementary ingredients to devise new models and algorithms for RBGs, aiming to boost methodological advancement in the field. We provide an overview of the software's key components and showcase a Knapsack Game, i.e., each player solves a binary knapsack problem. Code, documentation and examples are available at www.getzero.one.