Related papers: Ordinal Potential-based Player Rating

Ordinal Potential-based Player Rating

URL: http://arxiv.org/abs/2306.05366v4
Date: Wed, 6 Mar 2024 13:28:48 GMT
Title: Ordinal Potential-based Player Rating
Authors: Nelson Vadori and Rahul Savani
Abstract summary: We show that Elo ratings do preserve transitivity when computed in the right space. We introduce a new game decomposition that prioritises capturing the sign pattern of the game. 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.
Score: 6.454304238638547
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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