An extensive study of security games with strategic informants

Over the past years, game-theoretic modeling for security and public safety issues (also known as security games) have attracted intensive research attention and have been successfully deployed in many real-world applications for fighting, e.g., illegal poaching, fishing and urban crimes. However, few existing works consider how information from local communities would affect the structure of these games. In this paper, we systematically investigate how a new type of players – strategic informants who are from local communities and may observe and report upcoming attacks – affects the classic defender-attacker security interactions. Characterized by a private type, each informant has a utility structure that drives their strategic behaviors. For situations with a single informant, we capture the problem as a 3-player extensive-form game and develop a novel solution concept, Strong Stackelberg-perfect Bayesian equilibrium, for the game. To find an optimal defender strategy, we establish that though the informant can have infinitely many types in general, there always exists an optimal defense plan using only a linear number of patrol strategies; this succinct characterization then enables us to efficiently solve the game via linear programming. For situations with multiple informants, we show that there is also an optimal defense plan with only a linear number of patrol strategies that admits a simple structure based on plurality voting among multiple informants. Finally, we conduct extensive experiments to study the effect of the strategic informants and demonstrate the efficiency of our algorithm. Our experiments show that the existence of such informants significantly increases the defender's utility. Even though the informants exhibit strategic behaviors, the information they supply holds great value as defensive resources. Compared to existing works, our study leads to a deeper understanding on the role of informants in such defender-attacker interactions.