Game Theoretic Formation Design for Probabilistic Barrier Coverage

We study strategies to deploy defenders/sensors to detect intruders that approach a targeted region. This scenario is formulated as a barrier coverage, which aims to minimize the number of unseen paths. The problem becomes challenging when the number of defenders is insufficient for a full coverage, requiring us to find the most effective location to deploy them. To this end, we use ideas from game theory to account for various paths that the intruders may take. Specifically, we propose an iterative algorithm to refine the set of candidate defender formations, which uses the payoff matrix to directly evaluate the utility of different formations. Given the set of candidate formations, a mixed Nash equilibrium gives a stochastic policy to deploy the defenders. The efficacy of the proposed strategy is demonstrated by a numerical analysis that compares our method with an existing graph-theoretic method.