A coding theoretic study of homogeneous Markovian predictive games

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Nomura, Takara, Fujiwara, Akio
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913678037614592
author Nomura, Takara
Fujiwara, Akio
author_facet Nomura, Takara
Fujiwara, Akio
contents 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 Leó Szilárd's thought experiment.
format Preprint
id arxiv_https___arxiv_org_abs_2502_02433
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A coding theoretic study of homogeneous Markovian predictive games
Nomura, Takara
Fujiwara, Akio
Information Theory
Computer Science and Game Theory
Probability
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 Leó Szilárd's thought experiment.
title A coding theoretic study of homogeneous Markovian predictive games
topic Information Theory
Computer Science and Game Theory
Probability
url https://arxiv.org/abs/2502.02433