A search game with one object and two searchers

Nakai, Teruhisa

doi:10.2307/3214008

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…A searcher gets payoff 1 if he is the unique player to find the hider; 1/2 if both searchers find the hider at the same time and 0 if the other searcher finds the hider alone. This element of competition between the searchers has been studied in Nakai [ 23 ] and Duvocelle [ 12 ], but here the hider is also adversarial. Figure 6 shows the five states.…”

Section: Three Agents On the Cycle Graphmentioning

confidence: 99%

Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks

Alpern

Zeng

2022

Dyn Games Appl

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During epidemics, the population is asked to socially distance, with pairs of individuals keeping two meters apart. We model this as a new optimization problem by considering a team of agents placed on the nodes of a network. Their common aim is to achieve pairwise graph distances of at least D, a state we call socially distanced. (If $$D=1,$$ D = 1 , they want to be at distinct nodes; if $$D=2$$ D = 2 they want to be non-adjacent.) We allow only a simple type of motion called a lazy random walk: with probability p (called the laziness parameter), they remain at their current node next period; with complementary probability $$1-p$$ 1 - p , they move to a random adjacent node. The team seeks the common value of p which achieves social distance in the least expected time, which is the absorption time of a Markov chain. We observe that the same Markov chain, with different goals (absorbing states), models the gathering, or multi-rendezvous problem (all agents at the same node). Allowing distinct laziness for two types of agents (searchers and hider) extends the existing literature on predator–prey search games to multiple searchers. We consider only special networks: line, cycle and grid.

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Section: Three Agents On the Cycle Graphmentioning

confidence: 99%

Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks

Alpern

Zeng

2022

Dyn Games Appl

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“…For multi-player search games, in which all players have distribution strategies of their resources, [182] applied the name of search-search game (SSG). However, a similar such game used to be called a Blotto game (BG) even though that name is not used solely by search games.…”

Section: Search-search Blotto and Attack-defense Gamesmentioning

confidence: 99%

“…We have examined the following studies on SSGs from the context of search game. [182] dealt with a noncooperative TPZS game that involved two searchers, each of which has an independent estimation on the hider's distribution probability. The hider conceals himself in n cells, and the each searcher works to maximize his or her hider detection probability before it is detected by the competing searcher.…”

Section: Search-search Blotto and Attack-defense Gamesmentioning

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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“…Croucher (1975) solves a detection search model under the opponent's distrubance as a zero-sum game. Nakai (1986) considers a preemptive detection model for one common object by two searchers and formulates it by a non zero-sum game. He obtains a Nash equilibrium solution of this game in the form of a solution of a certain simultaneous differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Preemptive Detection Game

Nakai

1990

Journal of Information and Optimization Sciences

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We consider a zero-sum search game in which two players search for different stationary objects respectively and compete for the earlier detection than the opponent under the condition that the search effort allocated by one player diminishes the effect of the opponent's search each other. A necessary condition for a strategy to be optimal and an important property are derived. Furthermore in no disturbance case we show that the optimal strategy for each player is the same as the optimal search policy for the detection search problem by only one player.

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A search game with one object and two searchers

Cited by 12 publications

References 16 publications

Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks

Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks

Search Games: Literature and Survey

A Preemptive Detection Game

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