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.

翻译：本文研究了一种在完全图上进行的、具有N名玩家的离散时间部分并行动态噪声二元选择（伊辛）博弈，其中每时刻有k名玩家可能改变其策略，称为k-翻转伊辛博弈。文中给出了博弈转移矩阵的解析计算，以及分布φ=N⁺/N（其中N⁺为坚持两种策略之一的玩家数量）的前两阶矩。同时考虑了从亚稳态和不稳定态向稳定态跃迁的样本轨迹首次命中时间分布的前两阶矩。讨论了亚稳态衰变过程中这些矩对k的非平凡依赖关系。特定k*处极小值的出现归因于依赖k的扩散力与恢复力之间的竞争。