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The Indifference Character of Shot Strategies in a M versus N Duel(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1997年05期
Page:
93-96
Research Field:
Publishing date:

Info

Title:
The Indifference Character of Shot Strategies in a M versus N Duel
Author(s):
YangFang LiuLiwei ①
Department of Mathematics,CMU,Nanjing 210009)
Keywords:
operat ions r esearch stochast ic f ire pr obability duel applied probability
PACS:
E920.2
DOI:
-
Abstract:
Suppose that the two sides in a duel are sideA and side B and that side A has M w eapons o f the same kind and side B has N w eapons of the same kind. Both sides may dif fer in their w eapons. Let X A be the firing time inter vals o f a w eapon of side A and X B be tho se o f a w eapon of side B , and X A ~ ne d( r A ) , X B ~ ne d( rB ) . Also, N A ( t ) ( N B( t ) ) is the shot t imes o f one w eapon o f side A ( sideB ) in the t ime interval [ 0, t ) . Then, the paper can pr ove that N A ( t) ( N B( t ) ) is a poisson stochast ic process with the parameter rA ( r B) . U nder the assumpt ions stated abo ve, the paper prov ed that alternat io ns of shot st rateg ies in either side can neither increase nor decr ease it s w inning probability in the duel . In the situat ion like this, it means that there are no so-called opt imum shot st rateg ies for bo th sides.

References:

1 盛聚. 概率论与与数理统计. 北京: 高等教育出版社, 1989. 93, 307, 312
2 Kikuta K. T he matr ix game derived fr om the many-against -many battle. Nav al Resear ch Logistics Qua rter ly, 1986. 603~606
3 沈海玉. 随机格斗理论. 北京: 国防工业出版社, 1989. 206~207

Memo

Memo:
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Last Update: 2013-03-29