A coding theoretic study of homogeneous Markovian predictive games
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| 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 |