Weighted search games

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

doi:10.1016/j.ejor.2008.02.007

Cited by 16 publications

(4 citation statements)

References 14 publications

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“…Game theory has been used to analyze some other problems related to patrol problems, such as search games and infiltration games. In search games, a searcher seeks to find a hider who does not want to be found Gal 2002, 2003;Thomas and Washburn 1991;Zoroa et al 2009). In infiltration games, an intruder wants to penetrate an area without being caught by the guard (Auger 1991;Kikuta 2004, 2009;Ruckle 1983;Washburn and Wood 1995).…”

Section: Introductionmentioning

confidence: 99%

A Graph Patrol Problem with Random Attack Times

Lin

Atkinson

Chung

et al. 2013

Operations Research

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This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and strategic attackers. A random attacker chooses which node to attack according to a probability distribution known to the patroller. A strategic attacker plays a two-person zero-sum game with the patroller. For each case, we give an exact linear program to compute the optimal solution. Because the linear programs quickly become computationally intractable as the problem size grows, we develop index-based heuristics. In the random-attacker case, our heuristic is optimal when there are two nodes, and in a suitably chosen asymptotic regime. In the strategic-attacker case, our heuristic is optimal when there are two nodes if the attack times are deterministic taking integer values. In our numerical experiments, our heuristic typically achieves within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy.

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Section: Introductionmentioning

confidence: 99%

A Graph Patrol Problem with Random Attack Times

Lin

Atkinson

Chung

et al. 2013

Operations Research

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“…We have examined other research papers that discuss AGs on a lattice, such as Zoroa and Zoroa (1993) [251] and Zoroa and Fernandez-Saez (2001) [247]. Zoroa et al (2009) [252] considered a game with the payoff weighted by invasion points.…”

Section: Ambush Gamementioning

confidence: 99%

Search Games: Literature and Survey

Hohzaki

2016

JORSJ

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The purpose of this paper is to review literature published to date on search games, almost all of which have originated from search theory. Search theory itself is a research field of operations research that arose from realistic research efforts into air defense operations in England during World War II while the concept of search theory originated in anti-submarine warfare operations conducted by the U.S. Navy against German U-boats during the same war. The search game is an application of game theory to search problems in search theory. Search games have two main players: searchers and targets. There are some models in the search game: binary search game, linear search game, hide-search game, hide-allocation game, evasion-search game, princess-monster game, ambush game, search allocation game, path-constrained search game and search-search game. We fully survey literature on these models. We also outline other games which are closely related to the search game. Search theory has been evolving to be not method-oriented but problem-oriented for practical applications. Therefore we focus on the description of the discovery of problems and their modeling in this paper while we seldom mention the methodologies the authors devised for their search problems.

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“…Djemani et al (2000) gives related empirical work on search problems between a host and a parasitoid. Other recent work on search games includes the more abstract work of Evans and Bishop (2013) and the operational research related approach of Zoroa et al (2009Zoroa et al ( , 2012. The two monographs on search games are Garnaev (2000) and Alpern and Gal (2003).…”

Section: Introductionmentioning

confidence: 99%

“…The two monographs on search games are Garnaev (2000) and Alpern and Gal (2003). Related work on patrolling is given in Lin et al (2013) and Zoroa (2009). Connections with inspection and smuggling games are mentioned in Section 5, on a discrete version of our game.…”

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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Weighted search games

Cited by 16 publications

References 14 publications

A Graph Patrol Problem with Random Attack Times

A Graph Patrol Problem with Random Attack Times

Search Games: Literature and Survey

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

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