2023/06/08 by Nelson Vadori, Rahul Savani, Vadori, Nelson +1
Computer Science · Economics, Econometrics and Finance · #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Reinforcement Learning in Robotics #Sports Analytics and Performance
paper · pdf · doi:10.48550/arxiv.2306.05366
openalex publication_date 2023/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was recently observed that Elo ratings fail at preserving transitive relations among strategies and therefore cannot correctly extract the transitive component of a game. We provide a characterization of transitive games as a weak variant of ordinal potential games and show that Elo ratings actually do preserve transitivity when computed in the right space, using suitable invertible mappings. Leveraging this insight, we introduce a new game decomposition of an arbitrary game into transitive and cyclic components that is learnt using a neural network-based architecture and that prioritises capturing the sign pattern of the game, namely transitive and cyclic relations among strategies. We link our approach to the known concept of sign-rank, and evaluate our methodology using both toy examples and empirical data from real-world games.