We develop a model of the multi-agent perimeter-defense game to calculate how
an adaptive defense should be organized. This model is inspired by the human
immune system and captures settings such as heterogeneous teams, limited
resource allocations, partial observability of the attacking side, and
decentralization. An optimal defense, that minimizes the harm under constraints
of the energy spent to maintain a large and diverse repertoire, must maintain
coverage of the perimeter from a diverse attacker population. The model
characterizes how a defense might take advantage of its ability to respond
strongly to attackers of the same type but weakly to attackers of diverse types
to minimize the number of diverse defenders and while reducing harm. We first
study the model from a steady-state perimeter-defense perspective and then
extend it to mobile defenders and evolving attacker distributions. The optimal
defender distribution is supported on a discrete set and similarly a Kalman
filter obtaining local information is able to track a discrete, sometimes
unknown, attacker distribution. Simulation experiments are performed to study
the efficacy of the model under different constraints.Comment: 8 pages, 6 figure