Cops and Robbers games have been studied for the last few decades in computer science and mathematics. As in general pursuit evasion games, pursuers (cops) seek to capture evaders (robbers); however, players move in turn and are constrained to move on a discrete structure, usually a graph, and know the exact location of their opponent. In 2017, Bonato and MacGillivray [2] presented a general characterization of Cops and Robbers games in order for them to be globally studied. However, their model doesn't cover cases where stochastic events may occur, such as the robbers moving in a random fashion. In this paper we present a novel model with stochastic elements that we call a Generalized Probabilistic Cops and Robbers game (GPCR). A typical such game is one where the robber moves according to a probabilistic distribution, either because she is rather lost or drunk than evading, or because she is a robot. We present results to solve GPCR games, thus enabling one to study properties relating to the optimal strategies in large classes of Cops and Robbers games. Some classic Cops and Robbers games properties are also extended.

在过去的几十年里，计算机科学和数学一直在研究警察和强盗游戏。与一般的追捕逃避游戏一样，追捕者（警察）试图抓住逃避者（强盗）；然而，玩家依次移动并且被限制在离散结构（通常是图形）上移动，并且知道对手的确切位置。2017 年，Bonato 和 MacGillivray [2] 提出了 Cops and Robbers 游戏的一般特征，以便对其进行全球研究。但是，他们的模型不包括可能发生随机事件的情况，例如强盗以随机方式移动。在本文中，我们提出了一种具有随机元素的新模型，我们将其称为广义概率警察和强盗游戏 (GPCR)。典型的此类游戏是强盗根据概率分布移动的游戏，要么是因为她宁愿迷失或醉酒而不是逃避，要么是因为她是一个机器人。我们提出了解决 GPCR 游戏的结果，从而使人们能够研究与大类警察和强盗游戏中的最佳策略相关的属性。一些经典的警察和强盗游戏属性也得到了扩展。