A coding theoretic study of homogeneous Markovian predictive games
Information Theory
2025-02-05 v1 Computer Science and Game Theory
math.IT
Probability
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.
Keywords
Cite
@article{arxiv.2502.02433,
title = {A coding theoretic study of homogeneous Markovian predictive games},
author = {Takara Nomura and Akio Fujiwara},
journal= {arXiv preprint arXiv:2502.02433},
year = {2025}
}