On dynamic patrolling security games

Akifumi Kira, Naoyuki Kamiyama, Hirokazu Anai, Hiroaki Iwashita, Kotaro Ohori

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)152-168
Number of pages17
JournalJournal of the Operations Research Society of Japan
Issue number4
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


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