A search game with a protector

A search game with a protector A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval (1, n) in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λixi)) exp (−μiyi) when the searcher and protector allocate resources xi and yi respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Naval Research Logistics: An International Journal Wiley

A search game with a protector

Loading next page...
 
/lp/wiley/a-search-game-with-a-protector-LiV4zSn1ZT
Publisher site
See Article on Publisher Site

Abstract

A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval (1, n) in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λixi)) exp (−μiyi) when the searcher and protector allocate resources xi and yi respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000

Journal

Naval Research Logistics: An International JournalWiley

Published: Mar 1, 2000

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off