Continuous patrolling and hiding games

• Published in: European journal of operational research Vol. 277; no. 1; pp. 42 - 51
• Main Author: Garrec, Tristan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-08-2019; Elsevier
• Subjects: Computer Science; Games theory; Military; Networks; Noncooperative; Search/surveillance; Networks; Noncooperative; Search/surveillance; Games theory; Military
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2019.02.026

•Existence of the value and general upper bound.•Value and optimal strategies of continuous patrolling games on Eulerian networks.•Asymptotic expression of the value of continuous patrolling games on R2.•Study of the three parallel arcs network.•Asymptotic value of hiding games on positive Lebesgue measure search spaces.
We present two zero-sum games modeling situations where one player attacks (or hides in) a finite dimensional nonempty compact set, and the other tries to prevent the attack (or find him). The first game, called patrolling game, corresponds to a dynamic formulation of this situation in the sense that the attacker chooses a time and a point to attack and the patroller chooses a continuous trajectory to maximize the probability of finding the attack point in a given time. Whereas the second game, called hiding game, corresponds to a static formulation in which both the searcher and the hider choose simultaneously a point and the searcher maximizes the probability of being at distance less than a given threshold of the hider.