A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco

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.