Using Game Theory Approach for Assessment of Risk and Police Patrols Scheduling

Abstract

This study proposes a two-step game theory model framework for the purpose of scheduling police patrol shifts. In the first step, the three important factors of interaction between criminals and police are modeled as a zero-sum noncooperative game, and the risk value of each patrol area is obtained by calculating the mixed strategy Nash equilibrium. In the second step, the Shapley values of three different threat levels are calculated according to the rates of criminal events within three time periods. Finally, the Shapley value is derived based on the three criminal threat levels for each district. A fair allocation of police personnel based on the Shapley value is made with a minimum set of personnel deployment costs. This study used the 2016 San Francisco Public Security Bureau's open data for consolidation and calculations to validate the model. The experimental results show that police planners can use this framework to quantitatively evaluate the criminal threat in each district when deciding upon the deployment of patrol officers for three shifts per day. Keywords—Nash equilibrium; Risk value; Shapley value; Patrol deployment 摘要—本方案结合了两种博弈理论模型,进而计算出各区 域每日三班的公安巡逻服务时间配置表。第 1 模型将各区域的 犯罪者与公安领导之间的互动关系建构成一场非合作零合博 奕,计算博奕的混合随机策略纳许均衡解,当作区域的安全 风险值。第 2 模型根据公安局记录所有发生案件的次数,计算 三个时段发生案件次数的比例,当作三个安全警示等级的三 个门坎值,依三个不同安全警示等级的门坎值,计算所有区 域安全威胁值的结盟数值,并得出每一区域的夏普利值 (Shapley value)。最后,将各区域的夏普利值乘上每日三班 次的公安巡逻人员总数,即产出 10 区域每日三班次的公安巡 逻班表。本研究利用 2016 年旧金山市公安局的开放数据验证 本模型。实验结果显示,在现有的公安巡逻警力下,可以有 效的分配整体三时段的巡逻班表。公安部门管理者应用本架 构可以量化评估那个区域是较危险?以增加公安部门处理犯 罪发生时的反应能力。 关键词—纳许均衡,风险值,夏普利值,巡逻配置 I. 引言 公安资源有限的城市里,公安局(Police Department) 能在任何时间提供完善充分的安全覆盖是一个极具挑战 性的任务。愈来愈多随机性的犯罪活动,使得公安编组 巡逻的安排更加困难,唯有建立优化的公安巡逻时间表, 才能减少潜在的犯罪行为发生。在图 1 中,公安巡逻存 在着资源分配的困境,当部署公安越多,巡逻愈频繁, 巡逻人力及装备耗用的成本就越高,大规模部署往往会 浪费资源,反而会让都市安全威胁(风险)提升;然而, 部署公安太少,巡逻次数太少,或遗漏了重点地区,只 会让犯罪者有机可乘,可能引发更多的犯罪事件,公安 局对于「提升破案能力」和「降低公安巡逻成本」之间 的困境无计可施[1]。因此,完备而适宜的公安巡逻计划, 必须找出公安巡逻数量和破案能力之间的平衡点,即以 最适宜的数量达到最大的破案能力。现行的巡逻排班缺 乏理性决策的具体措施,并没有应用数学模型来建构 「公安警力」和「辖区犯罪者」之间的互动行为。公安 局应该建构一套数据分析工具,它可以衡量每一区域的 犯罪活动强度(即犯罪率)和公安的破案能力(即破案 率),并需要考虑公安和犯罪者的行动效用(payoff), 以随机的巡逻策略,避免犯罪者能够预先观察公安巡逻 表中的漏洞。 Fourth Symposium on Disaster Risk Analysis and Management in Chinese Littoral Regions (DRAMCLR 2019) Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Intelligent Systems Research, volume 171