Dynamic Assignment Switching and Singular Surfaces in Multi-Agent Pursuit-Evasion Games

G. Das, Y. Lee, A. Von Moll, D. Maity, M. Dorothy, E. Bakolas, and D. Shishika

Published in Transactions on Automatic Control (Submitted for Review), 2026

Motivated by border-defense, this paper stud- ies a pursuit-evasion game between two pursuers and two evaders where the payoff of the game is the sum of evaders’ y-coordinates at their respective capture times. From the literature we know that an assignment-based strategy achieves saddle-point equilibrium, provided that pursuers commit to a fixed assignment at the initial time and maintain it throughout the game. We relax this assump- tion and investigate scenarios where pursuers may dy- namically switch assignments based on the evolving game state. We first derive a closed-form characterization of the Assignment Switching Singular Surface (AS3). Under fixed assignments, AS3 behaves as a “dispersal” surface without inducing chattering behavior. However, when dynamic as- signment switching is permitted, the previously established open-loop value of the game no longer represents saddle- point equilibrium. Rather, pursuers dynamically switching assignments can guarantee payoffs strictly exceeding the open-loop value of the game, while evaders cannot bound payoffs below it. To address this asymmetry, we propose a Stackelberg evader strategy that provides computable per- formance bounds for both teams, establishing tight bounds on the true value of the game under dynamic assignment switching.