Security Games with Probabilistic Constraints on the Agent's Strategy

This paper considers a special case of security games dealing with the protection of a large area divided in multiple cells for a given planning period. An intruder decides on which cell to attack and an agent selects a patrol route visiting multiple cells from a finite set of patrol routes such that some given operational conditions on the agent’s mobility are met. For example, the agent might be required to patrol some cells more often than others. In order to determine strategies for the agent that deal with these conditions and remain unpredictable for the intruder, this problem is modeled as a two-player zero-sum game with probabilistic constraints such that the operational conditions are met with high probability. We also introduce a variant of the basic constrained security game in which the payoff matrices change over time, to allow for the payoff that may change during the planning period.