Ordinal Potential-based Player Rating

Vadori, Nelson and Savani, Rahul ORCID: 0000-0003-1262-7831 (2024) Ordinal Potential-based Player Rating .

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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.

Item Type:	Conference Item (Unspecified)
Divisions:	Faculty of Science & Engineering Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	21 Nov 2024 11:06
Last Modified:	23 May 2026 08:53
Related Websites:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3188061
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