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 "cross-reactivity" which enables a particular defender type to respond strongly to some attackers but weakly to a few different types of attackers. Due to this, the optimal defender distribution that minimizes the harm incurred by attackers is supported on a discrete set. This allows the defender team to allocate resources to a few types and yet tackle a large number of attacker types. 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, teams consisting of a small number of attackers and defenders, estimating and tackling an evolving attacker distribution, and competition between defenders that gives near-optimal behavior using decentralized computation of the control. We also compare this model with reinforcement-learned policies for the defender team.
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