{"ID":2830158,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.10389","arxiv_id":"2512.10389","title":"The $k$-flip Ising game","abstract":"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 $\\varphi=N^+/N$, 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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.10389","url_pdf":"https://arxiv.org/pdf/2512.10389v1","authors":"[\"Kovalenko Aleksandr\",\"Andrey Leonidov\"]","published":"2025-12-11T07:51:36Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"cond-mat.stat-mech\",\"physics.soc-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}