ON DYNAMIC PATROLLING SECURITY GAMES

We consider Stackelberg patrolling security games in which a security guard and an intruder walk around a facility. In these games, at each timepoint, the guard earns a reward (intruder incurs a cost) depending on their locations at that time. The objective of the guard (resp., the intruder) is to p...

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Bibliographic Details
Published inJournal of the Operations Research Society of Japan Vol. 62; no. 4; pp. 152 - 168
Main Authors Kira, Akifumi, Kamiyama, Naoyuki, Anai, Hirokazu, Iwashita, Hiroaki, Ohori, Kotaro
Format Journal Article
LanguageEnglish
Published Tokyo The Operations Research Society of Japan 31.10.2019
Nihon Opereshonzu Risachi Gakkai, Operations Research Society of Japan
Subjects
eye-catching patrol
Game theory
Games
Integer programming
Linear programming
Markov decision process
Markov processes
Mathematical programming
Mixed integer
Optimization
Patrols
Polynomials
Probability distribution
Security
time-expanded network
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Summary:We consider Stackelberg patrolling security games in which a security guard and an intruder walk around a facility. In these games, at each timepoint, the guard earns a reward (intruder incurs a cost) depending on their locations at that time. The objective of the guard (resp., the intruder) is to patrol (intrude) the facility so that the total sum of rewards is maximized (minimized). We study three cases: In Case 1, the guard chooses a scheduled route first and then the intruder chooses a scheduled route after perfectly observing the guard's choice. In Case 2, the guard randomizes her scheduled routes and then intruder observes its probability distribution and also randomize his scheduled routes. In Case 3, the guard randomizes her scheduled routes as well, but the intruder sequentially observes the location of the guard and reroutes to reach one of his targets. We show that the intruder's best response problem in Cases 1 and 2 and Case 3 can be formulated as a shortest path problem and a Markov decision process, respectively. Moreover, the equilibrium problem in each case reduces to a polynomial-sized mixed integer linear programming, linear programming, and bilinear programming problem, respectively.
ISSN:0453-4514
2188-8299
1878-6871
DOI:10.15807/jorsj.62.152