Abstract: An online system selects advertisements for presentation in various advertisement slots to maximize the total value to the online system for advertisement presentation. Candidate advertisements for presentation to a user are identified and types of advertisements are associated with various advertisement slots. For example, types of advertisements are associated with advertisement slots based on values for presenting various types of advertisements in different advertisement slots and one or more ad placement rules. Candidate advertisements having an advertisement type associated with each advertisement slot are identified, and an expected value of various placements of the candidate advertisements having a type corresponding to advertisement slots is determined. Based on the expected values, a placement of candidate advertisements in advertisement slots is selected and presented to a user.

Abstract: An online system selects advertisements for presentation in various advertisement slots to maximize the total value to the online system for advertisement presentation. Candidate advertisements for presentation to a user are identified and types of advertisements are associated with various advertisement slots. For example, types of advertisements are associated with advertisement slots based on values for presenting various types of advertisements in different advertisement slots and one or more ad placement rules. Candidate advertisements having an advertisement type associated with each advertisement slot are identified, and an expected value of various placements of the candidate advertisements having a type corresponding to advertisement slots is determined. Based on the expected values, a placement of candidate advertisements in advertisement slots is selected and presented to a user.

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: 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.