When Players Affect Target Values: Modeling and Solving Dynamic Partially Observable Security Games

Most of the current security models assume that the values of targets/areas are static or the changes (if any) are scheduled and known to the defender. Unfortunately, such models are not sufficient for many domains, where actions of the players modify the values of the targets. Examples include wildlife scenarios, where the attacker can increase value of targets by secretly building supporting facilities. To address such security game domains with player-affected values, we first propose DPOS3G, a novel partially observable stochastic Stackelberg game where target values are determined by the players’ actions; the defender can only partially observe these targets’ values, while the attacker can fully observe the targets’ values and the defender’s strategy. Second, we propose RITA (Reduced game Iterative Transfer Algorithm), which is based on the heuristic search value iteration algorithm for partially observable stochastic game (PG-HSVI) and introduces three key novelties: (a) building a reduced game with only key states (derived from partitioning the state space) to reduce the numbers of states and transitions considered when solving the game; (b) incrementally adding defender’s actions to further reduce the number of transitions; (c) providing novel heuristics for lower bound initialization of the algorithm. Third, extensive experimental evaluations of the algorithms show that RITA significantly outperforms the baseline PG-HSVI algorithm on scalability while allowing for trade off in scalability and solution quality.