Abstract: Different solution methodologies for addressing problems or issues when directing security domain patrolling strategies according to attacker-defender Stackelberg security games. One type of solution provides for computing optimal strategy against quantal response in security games, and includes two algorithms, the GOSAQ and PASAQ algorithms. Another type of solution provides for a unified method for handling discrete and continuous uncertainty in Bayesian Stackelberg games, and introduces the HUNTER algorithm. Another solution type addresses multi-objective security games (MOSG), combining security games and multi-objective optimization. MOSGs have a set of Pareto optimal (non-dominated) solutions referred to herein as the Pareto frontier. The Pareto frontier can be generated by solving a sequence of constrained single-objective optimization problems (CSOP), where one objective is selected to be maximized while lower bounds are specified for the other objectives.

Abstract: Efficient heuristic methods are described for approximating the optimal leader strategy for security domains where threats come from unknown adversaries. These problems can be modeled as Bayes-Stackelberg games. An embodiment of the heuristic method can include defining a patrolling or security domain problem as a mixed-integer quadratic program. The mixed-integer quadratic program can be converted to a mixed-integer linear program. For a single follower (e.g., robber or terrorist) scenario, the mixed-integer linear program can be solved, subject to appropriate constraints. For embodiments applicable to multiple follower situations, the relevant mixed-integer quadratic program and related mixed-integer linear program can be decomposed, e.g., by changing the response function for the follower from a pure strategy to a weighted combination over various pure follower strategies where the weights are probabilities of occurrence of each of the follower types.

Abstract: Efficient heuristic methods are described for approximating the optimal leader strategy for security domains where threats come from unknown adversaries. These problems can be modeled as Bayes-Stackelberg games. An embodiment of the heuristic method can include defining a patrolling or security domain problem as a mixed-integer quadratic program. The mixed-integer quadratic program can be converted to a mixed-integer linear program. For a single follower (e.g., robber or terrorist) scenario, the mixed-integer linear program can be solved, subject to appropriate constraints. For embodiments applicable to multiple follower situations, the relevant mixed-integer quadratic program and related mixed-integer linear program can be decomposed, e.g., by changing the response function for the follower from a pure strategy to a weighted combination over various pure follower strategies where the weights are probabilities of occurrence of each of the follower types.

Abstract: Techniques are described for Stackelberg games, in which one agent (the leader) must commit to a strategy that can be observed by other agents (the followers or adversaries) before they choose their own strategies, in which the leader is uncertain about the types of adversaries it may face. Such games are important in security domains, where, for example, a security agent (leader) must commit to a strategy of patrolling certain areas, and robbers (followers) have a chance to observe this strategy over time before choosing their own strategies of where to attack. An efficient exact algorithm is described for finding the optimal strategy for the leader to commit to in these games. This algorithm, Decomposed Optimal Bayesian Stackelberg Solver or “DOBSS,” is based on a novel and compact mixed-integer linear programming formulation. The algorithm can be implemented in a method, software, and/or system including computer or processor functionality.

Abstract: Efficient heuristic methods are described for approximating the optimal leader strategy for security domains where threats come from unknown adversaries. These problems can be modeled as Bayes-Stackelberg games. An embodiment of the heuristic method can include defining a patrolling or security domain problem as a mixed-integer quadratic program. The mixed-integer quadratic program can be converted to a mixed-integer linear program. For a single follower (e.g., robber or terrorist) scenario, the mixed-integer linear program can be solved, subject to appropriate constraints. For embodiments applicable to multiple follower situations, the relevant mixed-integer quadratic program and related mixed-integer linear program can be decomposed, e.g., by changing the response function for the follower from a pure strategy to a weighted combination over various pure follower strategies where the weights are probabilities of occurrence of each of the follower types.

Abstract: Efficient heuristic methods are described for approximating the optimal leader strategy for security domains where threats come from unknown adversaries. These problems can be modeled as Bayes-Stackelberg games. An embodiment of the heuristic method can include defining a patrolling or security domain problem as a mixed-integer quadratic program. The mixed-integer quadratic program can be converted to a mixed-integer linear program. For a single follower (e.g., robber or terrorist) scenario, the mixed-integer linear program can be solved, subject to appropriate constraints. For embodiments applicable to multiple follower situations, the relevant mixed-integer quadratic program and related mixed-integer linear program can be decomposed, e.g., by changing the response function for the follower from a pure strategy to a weighted combination over various pure follower strategies where the weights are probabilities of occurrence of each of the follower types.

Abstract: Techniques are described for Stackelberg games, in which one agent (the leader) must commit to a strategy that can be observed by other agents (the followers or adversaries) before they choose their own strategies, in which the leader is uncertain about the types of adversaries it may face. Such games are important in security domains, where, for example, a security agent (leader) must commit to a strategy of patrolling certain areas, and robbers (followers) have a chance to observe this strategy over time before choosing their own strategies of where to attack. An efficient exact algorithm is described for finding the optimal strategy for the leader to commit to in these games. This algorithm, Decomposed Optimal Bayesian Stackelberg Solver or “DOBSS,” is based on a novel and compact mixed-integer linear programming formulation. The algorithm can be implemented in a method, software, and/or system including computer or processor functionality.