A generalization of Ruckle's results for an ambush game

Zoroa, Noemí; Zoroa, P.; Fernández-Sáez, María-José

doi:10.1016/s0377-2217(99)00137-x

Cited by 13 publications

(12 citation statements)

References 3 publications

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“…where r is an integer 0 < r < p (5) or N = (r + p)q, where r is an integer 0 < r < q, where I = {1, 2, . .…”

Section: Case Where P and Q Are Coprimementioning

confidence: 99%

“…Ruckle [4], Baston and Bostock [1], Lee [3], and Zoroa, Zoroa, and Fernández-Sáez [5] investigated a continuous version of this problem where the cables have lengths a and b (a ≤ b) and the channel has unit width. Ruckle [4] solved this game for the cases (i) a = b, (ii) a = 1 3 , b = 1 2 , and (iii) a = 1 5 , b = 1 2 .…”

Section: Introductionmentioning

confidence: 99%

“…Baston and Bostock [1] gave a complete solution when b ≥ 1 2 and for some general cases when b < 1 2 . Lee [3] gave the solution for the case 1 3 ≤ b < 1 2 , and Zoroa, Zoroa, and Fernández-Sáez [5] obtain the solution for several general situations not included in [1], [3], and [4]. In this continuous version the roles of both players are interchanged, so that they study the problem from the point of view of the ambush games.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New results on a Ruckle problem in discrete games of ambush

Zoroa

Fernndez-Sez

2001

Naval Research Logistics

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“…where r is an integer 0 < r < p (5) or N = (r + p)q, where r is an integer 0 < r < q, where I = {1, 2, . .…”

Section: Case Where P and Q Are Coprimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New results on a Ruckle problem in discrete games of ambush

Zoroa

Fernndez-Sez

2001

Naval Research Logistics

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“…Originally introduced for search games in Alpern and Asic (1986), various forms of ambush problems have been explored in Baston and Bostock (1987), Hohzaki and Iida (2001), Baston and Kikuta (2004), and Zoroa et al (1999Zoroa et al ( , 2011. In the predator-prey context, the ambush mode of certain predators is often called the 'sit-and-wait' strategy.…”

Section: Introductionmentioning

confidence: 99%

Optimal search and ambush for a hider who can escape the search region

Alpern

Fokkink

Simanjuntak

2016

European Journal of Operational Research

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Search games for a mobile or immobile hider traditionally have the hider permanently con…ned to a compact 'search region'making eventual capture inevitable. Hence the payo¤ can be taken as time until capture. However in many real life search problems it is possible for the hider to escape an area in which he was known to be located (e.g. Bin Laden from Tora Bora) or for a prey animal to escape a predator's hunting territory. We model and solve such continuous time problems with escape where we take the probability of capture to be the searcher's payo¤.We assume the searcher, while cruise searching, can cover the search region at unit rate of area, for a given time horizon T known to the hider. The hider can stay still or choose any time to ‡ee the region. To counter this, the searcher can also adopt an ambush mode which will capture a ‡eeing hider. The searcher wins the game if he either …nds the hider while cruise searching or ambushes him while he is attempting to ‡ee; the hider wins if he ‡ees successfully (while the searcher is cruising) or has not been found by time T: The optimal searcher strategy involves decreasing the ambush probability over time, to a limit of zero. This surprising behaviour is opposite to that found recently by Alpern et al (2011Alpern et al ( , 2013 in a predator-prey game with similar dynamics but without the possibility of the hider escaping. Our work also complements that of Zoroa et al (2014) on searching for multiple prey and Gal and Casas (2014) for a combined model of search and pursuit.

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“…Such a game, in its most basic form, involves the crossing of a continuous interval in which an attacker can place ambushes, as in Ruckle (1983) and Zoroa et al (1999).…”

Section: Introductionmentioning

confidence: 99%

Ambush avoidance in vehicle routing for valuable delivery

2010

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In this work we consider route planning for valuable delivery in an urban environment under the threat of ambushes in which a vehicle, starting from a depot, has to serve a set of predetermined destinations during the day. We provide a method to plan for hardly predictable multi-destination routing extending a minmax flow-based model available for single-destination cases. We then formulate the process of selecting a visiting order as a game to obtain a mixed routing strategy. We analyse the application of the method to a set of simulation scenarios and compare the mixed routing strategy against the best routing. Finally we develop further the methodology introducing a second-level optimization model which reduces the overall risk associated to the proposed mixed routing strategy.2

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A generalization of Ruckle's results for an ambush game

Cited by 13 publications

References 3 publications

New results on a Ruckle problem in discrete games of ambush

New results on a Ruckle problem in discrete games of ambush

Optimal search and ambush for a hider who can escape the search region

Ambush avoidance in vehicle routing for valuable delivery

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