A search game with a protector

✍ Scribed by V.J. Baston; A.Y. Garnaev

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 123 KB
• Volume: 47
• Category: Article
• ISSN: 0894-069X
• DOI: 10.1002/(sici)1520-6750(200003)47:2<85::aid-nav1>3.0.co;2-c

✦ Synopsis

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(-λ ixi)) 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.