A remark on a helicopter and submarine game

✍ Scribed by Andrej Y U. Garnaev

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 350 KB
• Volume: 40
• Category: Article
• ISSN: 0894-069X
• DOI: 10.1002/1520-6750(199308)40:5<745::aid-nav3220400514>3.0.co;2-1

✦ Synopsis

The article considers a two-person zero-sum game in which the movement of the players is constrained to integer points . . . , -1, 0, 1, . . . of a line L. Initially the searcher (hider) is at point x = 0 (x = d, d > 0). The searcher and the hider perform simple motion on L with maximum speeds w and u , respectively, where w > u > 0. Each of the players knows the other's initial position but not the other's subsequent positions. The searcher has a bomb which he can drop at any time during his search. Between the dropping of the bomb and the bomb exploding there is a T time lag. If the bomb explodes at point i and the hider is at point i -1, or i, or i + 1, then the destruction probability is equal to P , or 1, or P , respectively, where 0 < P < 1. d, w , u , and T are integer constants. The searcher can drop the bomb at integer moments of time t = 0, 1, . . . . The aim of the searcher is to maximize the probability of the destruction of the hider. 0 1993 John Wiley 6i Sons, Inc.