Riemannian game dynamics

• 成果类型: Article
• 署名作者: Mertikopoulos, Panayotis; Sandholm, William H.
• 署名单位: Inria; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2018.06.002
• 发表日期: 2018
• 页码: 315-364
• 关键词: Evolutionary game theory; learning in games; Projection dynamics; Riemannian metrics; Replicator dynamics; Reinforcement Learning

摘要

We study a class of evolutionary game dynamics defined by balancing a gain determined by the game's payoffs against a cost of motion that captures the difficulty with which the population moves between states. Costs of motion are represented by a Riemannian metric, i.e., a state-dependent inner product on the set of population states. The replicator dynamics and the (Euclidean) projection dynamics are the archetypal examples of the class we study. Like these representative dynamics, all Riemannian game dynamics satisfy certain basic desiderata, including positive correlation, local stability of interior ESSs, and global convergence in potential games. When the underlying Riemannian metric satisfies a Hessian integrability condition, the resulting dynamics preserve many further properties of the replicator and projection dynamics. We examine the close connections between Hessian game dynamics and reinforcement learning in normal form games, extending and elucidating a well-known link between the replicator dynamics and exponential reinforcement learning. (C) 2018 Elsevier Inc. All rights reserved.