Ordinal Potential-based Player Rating

Nelson Vadori, Rahul Savani
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:118-126, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-vadori24a, title = {Ordinal Potential-based Player Rating}, author = {Vadori, Nelson and Savani, Rahul}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {118--126}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/vadori24a/vadori24a.pdf}, url = {https://proceedings.mlr.press/v238/vadori24a.html}, 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.} }
Endnote
%0 Conference Paper %T Ordinal Potential-based Player Rating %A Nelson Vadori %A Rahul Savani %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-vadori24a %I PMLR %P 118--126 %U https://proceedings.mlr.press/v238/vadori24a.html %V 238 %X 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.
APA
Vadori, N. & Savani, R.. (2024). Ordinal Potential-based Player Rating. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:118-126 Available from https://proceedings.mlr.press/v238/vadori24a.html.

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