Predicting Strategy of Rational Evader in Cooperative Pursuit: A Distributed Bimatrix Zero-sum Game Approach

Cooperative pursuit problems involve multiple pursuers cooperatively capturing an evader with a faster speed in an unbounded two-dimensional domain. To generate autonomous intelligent behaviors, pursuers must consider the responsive actions of the evader. Predicting the strategy of an evader often relies on the assumption that pursuers know full information, which is unrealistic. This paper proposes a strategy prediction method of multiple pursuers cooperating to predict a rational evader's strategy in a distributed game-theoretic framework. In this setup, each pursuer can only communicate with its neighbors and observe the evader's position, making the strategy prediction challenging. To tackle this issue, we model the strategy prediction problem as a bimatrix zero-sum game. Then, we propose a distributed Nash equilibrium seeking algorithm for such a game by combining the consensus averaging, the gradient tracking, and the Frank-Wolfe techniques. Furthermore, we integrate the strategy prediction into an existing cooperative pursuit method. Numerical simulations demonstrate that our method significantly improves the probability of successful capture compared to a state-of-the-art pursuit method.