# A search game on a cyclic graph

A search game on a cyclic graph 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 + examination cost) have geometrical relations depending on nodes. Then we give properties of optimal strategies of both players. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Naval Research Logistics: An International Journal Wiley

# A search game on a cyclic graph

17 pages

/lp/wiley/a-search-game-on-a-cyclic-graph-5ISuhSX4Xo
Publisher
Wiley
ISSN
0894-069X
eISSN
1520-6750
D.O.I.
10.1002/nav.20025
Publisher site
See Article on Publisher Site

### Abstract

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 + examination cost) have geometrical relations depending on nodes. Then we give properties of optimal strategies of both players. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

### Journal

Naval Research Logistics: An International JournalWiley

Published: Oct 1, 2004

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