Most violent crimes happen in urban and suburban cities. With emerging tracking techniques, law enforcement officers can have real-time location information of the escaping criminals and dynamically adjust the security resource allocation to interdict them. Unfortunately, existing work on urban network security games largely ignores such information. This paper addresses this omission. First, we show that ignoring the real-time information can cause an arbitrarily large loss of efficiency. To mitigate this loss, we propose a novel NEtwork purSuiT game (NEST) model that captures the interaction between an escaping adversary and a defender with multiple resources and real-time information available. Second, solving NEST is proven to be NP-hard. Third, after transforming the non-convex program of solving NEST to a linear program, we propose our incremental strategy generation algorithm, including: (i) novel pruning techniques in our best response oracle; and (ii) novel techniques for mapping strategies between subgames and adding multiple best response strategies at one iteration to solve extremely large problems. Finally, extensive experiments show the effectiveness of our approach, which scales up to realistic problem sizes with hundreds of nodes on networks including the real network of Manhattan.

Preventing crimes or terrorist attacks in urban areas is challenging. Law enforcement officers need to respond quickly to catch the attacker on his escape route, which is subject to time-dependent traffic conditions on transportation networks. The attacker can strategically choose his escape path and driving speed to avoid being captured. Existing work on security resource allocation has not considered such scenarios with time-dependent strategies for both players. Therefore, in this paper, we study the problem of efficiently scheduling security resources for interdicting the escaping attacker. We propose: 1) a new defender-attacker security game model for escape interdiction on transportation networks; and 2) an efficient double oracle algorithm to compute the optimal defender strategy, which combines mixed-integer linear programming formulations for best response problems and effective approximation algorithms for improving the scalability of the algorithms. Experimental evaluation shows that our approach significantly outperforms baselines in solution quality and scales up to realistic-sized transportation networks with hundreds of intersections.

Psychological experiment studies reveal that human interaction behaviors are often not the same as what game theory predicts. One of important reasons is that they did not put relevant constraints into consideration when the players choose their best strategies. However, in real life, games are often played in certain contexts where players are constrained by their capabilities, law, culture, custom, and so on. For example, if someone wants to drive a car, he/she has to have a driving license. Therefore, when a human player of a game chooses a strategy, he/she should consider not only the material payoff or monetary reward from taking his/her best strategy and others' best responses but also how feasible to take the strategy in that context where the game is played. To solve such a game, this paper establishes a model of fuzzily constrained games and introduces a solution concept of constrained equilibrium for the games of this kind. Our model is consistent with psychological experiment results of ultimatum games. We also discuss what will happen if Prisoner's Dilemma and Stag Hunt are played under fuzzy constraints. In general, after putting constraints into account, our model can reflect well the human behaviors of fairness, altruism, self‐interest, and so on, and thus can predict the outcomes of some games more accurate than conventional game theory.

In this paper, we develop a fuzzy dynamic belief revision logic system. In our system, propositions take truth values in a set of multiple fuzzy linguistic terms, which people use in everyday life. And we use a uninorm operator to aggregate the linguistic truth values of the same proposition but drawn from two different rules because uninorms can reflect well that the aggregated result of two somehow negative truth values of the same proposition should be more negative, the aggregated result of two somehow positive ones should be more positive, and the result of a negative one and a positive one is a compromise. In this system, the belief on a proposition is the linguistic truth of the proposition in the most possible world according to the current preference over all possible worlds. In the light of new information, the preference degrees of possible worlds will be updated. Accordingly, the most possible world will be changed to another and thus an old belief on a propositional formula will be changed to the linguistic truth of the proposition in the new most possible world. Moreover, we prove the soundness and completeness of our fuzzy dynamic belief revision system. In addition, we also prove that our belief revision method in fuzzy environment satisfies some relevant ones of standard AGM postulates (named after the names of their proponents, Alchourrón, Gärdenfors, and Makinson).

Bayesian games can handle the incomplete information about players' types. However, in real life, the information could be not only incomplete but also ambiguous for lack of sufficient evidence, i.e., a player cannot have a precise probability about each type of the other players. To address this issue, this paper firstly extends the Bayesian games to ambiguous Bayesian games. Then, we introduce the concept of a solution to this kind of games and discuss their properties, especially about solution existence, how the ambiguity degree and players' ambiguity attitude influence the outcomes of an ambiguous Bayesian game, the case of lower boundary probability, and the missing situation. We also illustrate our game model, especially in the public security domain. C 2014 Wiley Periodicals, Inc.