Leader-Follower Game Theory Approach for Adversarial Agents with Sensing Limitations

Game theory approaches, including those of the Stackelberg form, provide leader-follower strategies for agent patrolling. Specifically we use the developed approaches to agent patrolling in arbitrary spatial environments. The environment is discretized and has a topology structure of a directed graph. The patrolling agent follows a randomized patrol path along the graph. The adversarial agent desires to access certain target nodes in the graph and is assumed to take a certain amount of time to complete the intrusion of a target node. An optimization formulation with the structure constraints is used to provide a patroller strategy that maximizes its expected utility. Several issues arise in providing a game theory solution for an environment that affects sensor performance. Current minimax payoff models for sensing an adversary consider the probability for the defender to sense an adversary. For environmentally limited sensing, this term now has path dependence such as building interiors and areas with transmission issues. However the limitation of sensing was not previously considered and we have modified a constraint to consider this.