A coding theoretic study of homogeneous Markovian predictive games

Takara Nomura; Akio Fujiwara

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arXiv · 2502.02433

A coding theoretic study of homogeneous Markovian predictive games

Takara Nomura·Akio Fujiwara

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Abstract

This paper explores a predictive game in which a Forecaster announces odds based on a time-homogeneous Markov kernel, establishing a game-theoretic law of large numbers for the relative frequencies of occurrences of all finite strings. A key feature of our proof is a betting strategy built on a universal coding scheme, inspired by the martingale convergence theorem and algorithmic randomness theory, without relying on a diversified betting approach that involves countably many operating accounts. We apply these insights to thermodynamics, offering a game-theoretic perspective on Le\'o Szil\'ard's thought experiment.

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Takara Nomura, Akio Fujiwara. 2025-02-04. A coding theoretic study of homogeneous Markovian predictive games. https://arxiv.org/abs/2502.02433

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