Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations. We here show that similar noise-sustained trajectories arise in game dynamical learning, where the stochasticity has a different origin: agents sample a finite number of moves of their opponents in-between adaptation events. The limit of infinite batches results in deterministic modified replicator equations, whereas finite sampling leads to a stochastic dynamics. The characteristics of these fluctuations can be computed analytically using methods from statistical physics, and such noise can affect the attractors significantly, leading to noise-sustained cycling or removing periodic orbits of the standard replicator dynamics.
Collective evolutionary dynamical-systems games: Emergent turn-taking under anonymous monitoring
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（东北大学前沿跨学科研究院）；Computational Group Dynamics Collaboration Unit, RIKEN Center for Brain Science（理化学脑科学中心计算群体动力学合作单元）；The Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所）
