2025/02/04 by Takara Nomura, Nomura, Takara, Akio Fujiwara +1 · 1 voice
Computer Science · Decision Sciences · Mathematics · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Information Theory (cs.IT) #Probability (math.PR) #cs.GT #cs.IT #math.PR
paper · pdf · doi:10.48550/arxiv.2502.02433
openalex publication_date 2025/02/04 · arxiv published 2025/02/04 · arxiv updated 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.