The $k$-flip Ising game
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917138091999232 |
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| author | Aleksandr, Kovalenko Leonidov, Andrey |
| author_facet | Aleksandr, Kovalenko Leonidov, Andrey |
| contents | A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is considered. Analytical calculation of the transition matrix of game as well as the first two moments of the distribution of $φ=N^+/N$, where $N^+$ is a number of players adhering to one of the two strategies, is presented. First two moments of the first hitting time distribution for sample trajectories corresponding to transition from a metastable and unstable states to a stable one are considered. A nontrivial dependence of these moments on $k$ for the decay of a metastable state is discussed. A presence of the minima at certain $k^*$ is attributed to a competition between $k$-dependent diffusion and restoring forces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $k$-flip Ising game Aleksandr, Kovalenko Leonidov, Andrey Computer Science and Game Theory Statistical Mechanics Physics and Society A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is considered. Analytical calculation of the transition matrix of game as well as the first two moments of the distribution of $φ=N^+/N$, where $N^+$ is a number of players adhering to one of the two strategies, is presented. First two moments of the first hitting time distribution for sample trajectories corresponding to transition from a metastable and unstable states to a stable one are considered. A nontrivial dependence of these moments on $k$ for the decay of a metastable state is discussed. A presence of the minima at certain $k^*$ is attributed to a competition between $k$-dependent diffusion and restoring forces. |
| title | The $k$-flip Ising game |
| topic | Computer Science and Game Theory Statistical Mechanics Physics and Society |
| url | https://arxiv.org/abs/2512.10389 |