School of Computer Science and Software Engineering, Zhaoqing University, Guangdong, P. R. China.
Department of Information Management, National Central University, Taoyuan City, Taiwan.
Risk Anal. 2020 Mar;40(3):534-549. doi: 10.1111/risa.13411. Epub 2019 Oct 1.
An efficient police patrol schedule must ensure the allocation of an appropriate number of officers sufficient to respond to the danger of criminal incidents, particularly in an urban environment, even when the available number of personnel is limited. This study proposes a framework that incorporates two game theory models designed for the allocation of police officers to patrol shifts. In the first step, the interactions of three factors between the criminal and the operation captain are modeled as a zero-sum, noncooperative game, after which a mixed strategy Nash equilibrium method is used to derive the risk value for each district to be patrolled. In the second step, the risk values are used to compute the Shapley value for all 10 districts, for three different threat levels. A fair allocation of police personnel based on the Shapley value is made with a minimum set of personnel deployment costs. The efficacy of the proposed method is verified using openly available data from the San Francisco City Police detailing incidents from the year 2016. 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.
一个高效的警察巡逻时间表必须确保分配足够数量的警察，以应对犯罪事件的危险，特别是在城市环境中，即使可用的人员数量有限。本研究提出了一个框架，该框架结合了两种用于分配警察到巡逻班次的博弈论模型。在第一步中，将罪犯和行动队长之间的三个因素之间的相互作用建模为零和非合作博弈，然后使用混合策略纳什均衡方法得出每个要巡逻的区域的风险值。在第二步中，使用风险值为三种不同威胁级别计算所有 10 个区域的 Shapley 值。根据 Shapley 值进行公平的人员分配，部署人员的成本最小。使用旧金山市警察局详细记录 2016 年事件的公开可用数据验证了所提出方法的有效性。实验结果表明，警察规划者可以在每天部署三个班次的巡逻警察时，使用该框架来定量评估每个区域的犯罪威胁。
