A Search Game With Traveling Cost

Kikuta, Kensaku

doi:10.15807/jorsj.34.365

Cited by 23 publications

(14 citation statements)

References 5 publications

(6 reference statements)

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“…We ought to verify the equivalency between two problems (P 1 ) and (P T ). Since conditions (16), (17), and (18) evidently hold from definitions (15), we have a relation v 3 ≤ v 2 between optimal values of two problems. Conversely, we are going to show that ρ and ν(ξ ) are expressed by Eq.…”

Section: Derivation Of Equilibrium Pointmentioning

confidence: 99%

“…An optimal strategy of the searcher, ϕ * , is given by an optimal solution of (P S ) or optimal dual variables corresponding to condition (16) in (P T ). Similarly, an optimal strategy of the target, π * , is given by an optimal solution for (P T ) or optimal dual variables corresponding to condition (6) in (P S ).…”

Section: Derivation Of Equilibrium Pointmentioning

confidence: 99%

“…His problem was also a multistage game, with the payoff being the detection probability of the target. Kikuta [15,16] studied a game with the payoff of traveling cost. However, there have been not any research on a multistage dynamic search game in a continuous time space.…”

Section: Introductionmentioning

confidence: 99%

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A search game taking account of attributes of searching resources

Hohzaki

2007

Naval Research Logistics

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This article deals with a two-person zero-sum game called a search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. The effect of resources lasts a certain period of time and extends to some areas at a distance from the resources' dropped points. On the other hand, the target moves around in the search space to evade the searcher. In the history of search games, there has been little research covering the durability and reachability of searching resources. This article proposes two linear programming formulations to solve the SAG with durable and reachable resources, and at the same time provide an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. Using examples, we will analyze the influences of two attributes of resources on optimal strategies.

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Section: Derivation Of Equilibrium Pointmentioning

confidence: 99%

Section: Derivation Of Equilibrium Pointmentioning

confidence: 99%

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A search game taking account of attributes of searching resources

Hohzaki

2007

Naval Research Logistics

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“…Papers on the theory and practice of game theory can be found in operations research journals such as the Journal o f the Operations Research Society o f Japan [see, for example, Nakayama (1988), Kikuta (1990Kikuta ( , 1991, and Nakagami (1992)], Journal of the Operational Research Society, European Journal o f Operational Research, INFOR, and Operations Research. In reality, game theory methods have been developed and applied in virtually all fields in which multiple participant decision making is considered.…”

Section: Carrying Out Analysesmentioning

confidence: 99%

Game Theoretic Models in Engineering Decision Making

Hipel

Fang

Kilgour

1993

Doboku Gakkai Ronbunshu

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Various types of game theory models for systematically studying conflict in engineering and other fields are. reviewed, assessed, and illustrated. Representative literature regarding the development and application of game theory in engineering decision making is referenced and two applications are presented. Specifically, a game theory model in extensive form is employed to investigate the effectiveness of a commonly-practised system of environmental laws and regulations. In another application, the graph model for conflict resolution is used for modelling and analyzing a complex environmental dispute that took place in Canada. This conflict involves four main decision makers, each with its own objectives and priorities with respect to the controversy. To assist in formally analyzing the dispute and carrying out sensitivity analyses, a flexible decision support system is utilized.

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“…Kikuta [8] found a maximin solution in the same graph and in [9] he analyzed a maximin solution when the graph is a rooted tree and the seeker is at the root at the beginning. Gal [3] analyzed a maximin solution in which traveling costs are considered.…”

Section: Introductionmentioning

confidence: 99%

A search game on a cyclic graph

Kikuta

2004

Naval Research Logistics

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There is a finite cyclic graph. The hider chooses one of all nodes except the specified one, and he hides an (immobile) object there. At the beginning the seeker is at the specified node. After the seeker chooses an ordering of the nodes except the specified one, he examines each nodes in that order until he finds the object, traveling along edges. It costs an amount when he moves from a node to an adjacent one and also when he checks a node. While the hider wishes to maximize the sum of the traveling costs and the examination costs which are required to find the object, the seeker wishes to minimize it. The problem is modeled as a two-person zero-sum game. We solve the game when unit costs (traveling cost ϩ examination cost) have geometrical relations depending on nodes. Then we give properties of optimal strategies of both players.

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A Search Game With Traveling Cost

Abstract: The unique optimal strategy fbr the hider obtained in [6] can be compared with an a priori probability in G}uss [4]. The latter is proportionally increasing and the former is hyperboiically increasing as the label of a cell becomes large.

Cited by 23 publications

References 5 publications

A search game taking account of attributes of searching resources

A search game taking account of attributes of searching resources

Game Theoretic Models in Engineering Decision Making

A search game on a cyclic graph

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