We introduce a model for multi-agent interaction problems to understand how a heterogeneous team of agents should organize its resources to tackle a heterogeneous team of attackers. This model is inspired by how the human immune system tackles a diverse set of pathogens. The key property of this model is a "cross-reactivity" kernel which enables a particular defender type to respond strongly to some attacker types but weakly to a few different types of attackers. We show how due to such cross-reactivity, the defender team can optimally counteract a heterogeneous attacker team using very few types of defender agents, and thereby minimize its resources. We study this model in different settings to characterize a set of guiding principles for control problems with heterogeneous teams of agents, e.g., sensitivity of the harm to sub-optimal defender distributions, and competition between defenders gives near-optimal behavior using decentralized computation of the control. We also compare this model with existing approaches including reinforcement-learned policies, perimeter defense, and coverage control.
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