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.
We have designed a game theory based framework in order to compute effective agent asset laydown and courses of action (COAs) for adversarial scenarios. Our technical approach is based on Stackelberg security game theory, which is a specialization of game theory for adversarial situations and deterrence. Security games approaches provide a scalable optimization framework to determine geospatial COAs for agents. Specifically it can exploit intelligence about adversaries by constraining courses of action search and eliminating dominated COAs. Several issues arise in providing a game theory for a communication-constrained environment. Current minimax payoff models for sensing an adversary/obstacles consider the probability for the defender to sense an adversary. For limited acoustic sensing, this term now has path dependence such as building interiors and areas with transmission issues. Next, an extension to account for loss or degradation of defender assets is required. A candidate solution being considered is to have an agent update/choose degraded contingency strategies at each communication. We are also evaluating providing refined strategies as a function of time if communications are out and how to account for effect of uncertainty in our knowledge of agent member loss for updated strategies. We are employing simulators at NRL DC to model multiagent trajectories and allowing the testing of the game theory approach based on environmental conditions.
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