Abstract: The following information may be read from a memory system: an identification of each of multiple moving targets that are each expected to move in accordance with a schedule of when and where the target will move; the schedule; an identification of each of multiple mobile defense resources that each have a maximum movement speed and a maximum protection radius; and the maximum movement speed and the maximum protection radius of each mobile defense resource. A computer system may determine where each mobile defense resource should be at each of a sequential set of different times so as to optimize the ability of the mobile defense resources to protect each of the mobile targets from a single attack by an attacker against one of the targets at an unknown time based on the information read from the memory system. The determining may take into consideration that the attacker may observe and analyze movements of the mobile defense resources prior to the attack in formulating the attack.

Abstract: An optimized artificial intelligence machine may: receive information indicative of the times, locations, and types of crimes that were committed over a period of time in a geographic area; receive information indicative of the number and locations of patrol agents that were patrolling during the period of time; build a learning model based on the received information that learns the relationships between the locations of the patrol agents and the crimes that were committed; and determine whether and where criminals would commit new crimes based on the learning model and a different number of patrol agents or locations of patrol agents.

Abstract: The following information may be read from a memory system: an identification of each of multiple moving targets that are each expected to move in accordance with a schedule of when and where the target will move; the schedule; an identification of each of multiple mobile defense resources that each have a maximum movement speed and a maximum protection radius; and the maximum movement speed and the maximum protection radius of each mobile defense resource. A computer system may determine where each mobile defense resource should be at each of a sequential set of different times so as to optimize the ability of the mobile defense resources to protect each of the mobile targets from a single attack by an attacker against one of the targets at an unknown time based on the information read from the memory system. The determining may take into consideration that the attacker may observe and analyze movements of the mobile defense resources prior to the attack in formulating the attack.

Abstract: Game theory models may be used for producing a strategy and schedule for patrolling an area like a rail transportation system. In some instances, the model may account for events that cause a patrol unit to deviate from a patrol schedule and route. For example, a patrol schedule may be generated for one or more patrol units using a Bayesian Stackelberg game theory model based on a map of the public transportation system, a schedule of the transports, a list of the one or more patrolling units, a probability distribution for the occurrence of the passenger not paying to ride the transports, a list of the one or more possible events that would delay the patrol units, and a probability distribution for the occurrence of the one or more possible events that would delay the patrolling units represented by a Markov-decision process.

Abstract: A method and a system for resolving a two-player influencer blocking conflict are disclosed. The method and system may include to form a set of defender actions to increase a defender set of nodes; form a set of attacker actions; determine a defender strategy based the set of attacker actions, the defender strategy comprising a new defender action; to determine an attacker strategy that is based the set of defender actions; modify the set of defender actions to include the new defender action; update the set of attacker actions according to the attacker strategy; form a new set of attacker actions when the set of defender nodes increases more than a threshold; and form a display to show the defender set of nodes and the attacker set of nodes in a graph.

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.

Abstract: A system for coming up with policies of behavior for various agents engaged in a task. These policies consider costs and benefits of actions and outcomes, and uncertainties. The system utilizes limited neighborhoods of agents for expedited computing in large arrangements. Also sought are local and global optimums in terms of selecting policies.