Resource allocation in multi-layer, continuous defense, security games versus strategic attackers

When defending soft targets, such as airports, subway stations, sports venues and houses of worship, it is critical to optimally allocate defensive resources across the different security layers of multiple targets. This allocation will effectively utilize human and monetary resources and reduce the risks from attacks. In this problem the objective of the defender is to optimally allocate resources across multiple targets throughout the respective security layers to decrease the expected damages, decrease the probability of a successful attack, and potentially deter the adversary from executing an attack plan on any target. The attacker aims to circumvent the security measures by adaptively allocating resources across the different targets and layers. This paper expands on past resource allocation problems by demonstrating the extension of conclusions drawn of single-layer security systems to multi-layer cases when defending soft targets against adversarial threats. Through the results of this paper, we find that conclusions drawn from solving a 1-Layer resource allocation security game can be applied to a similar N − Layer game due to the way attackers are deterred in our game model. In addition, we find that several variables are interchangeable in our equilibrium solutions, meaning that it can be just as effective for the defender to adjust the value of their targets as it would be for them to adjust the inherent defense, which can be helpful in aiding the defender’s decision making process if they cannot or choose not to make changes to certain variables.