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


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The Indifference Character of Shot Strategies in a M versus N Duel
YangFang LiuLiwei ①
Department of Mathematics,CMU,Nanjing 210009)
operat ions r esearch stochast ic f ire pr obability duel applied probability
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.


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Last Update: 2013-03-29