{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/zero-playing-mathematical-programming-games","title":"ZERO: Playing Mathematical Programming Games","arxiv_id":"2111.07932","date":"2021-11-15","proceeding":null,"authors":["Gabriele Dragotto","Sriram Sankaranarayanan","Margarida Carvalho","Andrea Lodi"],"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.","url_abs":"https://arxiv.org/abs/2111.07932v2","url_pdf":"https://arxiv.org/pdf/2111.07932v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"zero-playing-mathematical-programming-games","repo_url":"https://github.com/ds4dm/zero","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}