{"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/-rank-multi-agent-evaluation-by-evolution","title":"α-Rank: Multi-Agent Evaluation by Evolution","arxiv_id":"1903.01373","date":"2019-03-04","proceeding":null,"authors":["Shayegan Omidshafiei","Christos Papadimitriou","Georgios Piliouras","Karl Tuyls","Mark Rowland","Jean-Baptiste Lespiau","Wojciech M. Czarnecki","Marc Lanctot","Julien Perolat","Remi Munos"],"abstract":"We introduce {\\alpha}-Rank, a principled evolutionary dynamics methodology,\nfor the evaluation and ranking of agents in large-scale multi-agent\ninteractions, grounded in a novel dynamical game-theoretic solution concept\ncalled Markov-Conley chains (MCCs). The approach leverages continuous-time and\ndiscrete-time evolutionary dynamical systems applied to empirical games, and\nscales tractably in the number of agents, in the type of interactions (beyond\ndyadic), and the type of empirical games (symmetric and asymmetric). Current\nmodels are fundamentally limited in one or more of these dimensions, and are\nnot guaranteed to converge to the desired game-theoretic solution concept\n(typically the Nash equilibrium). {\\alpha}-Rank automatically provides a\nranking over the set of agents under evaluation and provides insights into\ntheir strengths, weaknesses, and long-term dynamics in terms of basins of\nattraction and sink components. This is a direct consequence of our new model's\ndirect correspondence to the dynamical MCC solution concept when its\nranking-intensity parameter, {\\alpha}, is chosen to be large, which exactly\nforms the basis of {\\alpha}-Rank. In contrast to the Nash equilibrium, which is\na static solution concept based solely on fixed points, MCCs are a dynamical\nsolution concept based on the Markov chain formalism, Conley's Fundamental\nTheorem of Dynamical Systems, and the core ingredients of dynamical systems:\nfixed points, recurrent sets, periodic orbits, and limit cycles. Our\n{\\alpha}-Rank method runs in polynomial time with respect to the total number\nof pure strategy profiles, whereas computing a Nash equilibrium for a\ngeneral-sum game is known to be intractable. We introduce mathematical proofs\nthat reveal the formal underpinnings of the {\\alpha}-Rank methodology. We\nillustrate the method in canonical games and in AlphaGo, AlphaZero, MuJoCo\nSoccer, and Poker.","url_abs":"http://arxiv.org/abs/1903.01373v1","url_pdf":"http://arxiv.org/pdf/1903.01373v1.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":"abstracts"},"code_links":[{"paper_slug":"-rank-multi-agent-evaluation-by-evolution","repo_url":"https://github.com/deepmind/open_spiel","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"mathematical-proofs","task_name":"Mathematical Proofs"},{"task_slug":"mujoco","task_name":"MuJoCo"}],"methods":[{"method_slug":"alphazero","method_name":"AlphaZero"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1903.01373","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}