We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the payoff function is both shift-invariant and submixing, then the game is half-positional, i.e. the first player has an optimal strategy which is both deterministic and stationary. This result relies on the existence of epsilon-subgame-perfect strategies in shift-invariant games, a second contribution of the paper. The techniques can be used to establish a third result: for shift-invariant and submixing payoff functions, the existence of finite-memory strategies for player 2 in one-player games implies the same property for two-player games as well.
Language-based game theory in the age of artificial intelligence
University of Milan Bicocca（米兰比可卡大学）；University of Parma（帕尔马大学）；University of Maribor（马里博尔大学）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔克博士社区卫生中心）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；Kyung Hee University（庆熙大学）；University of Bologna（博洛尼亚大学）
RSD-Poker: Structure-Adaptive and Shift-Robust Risk-Utility Certification for Residual Policies in Imperfect-Information Games
School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）
