LINEAR-ACCURACY ONE-BULLET SILENT DUEL WITH PROGRESSING-BY-ONE-THIRD SHOOTING MOMENTS
DOI:
https://doi.org/10.20535/kpisn.2025.4.343114Keywords:
one-bullet silent duel, linear accuracy, matrix game, pure strategy solution, progressing-by-one-third shooting momentsAbstract
Background. A finite zero-sum game is considered, which models competitive interaction between two subjects. The subject, referred to as the duelist, must take an action (or, metaphorically, shoot the single bullet) during a standardized time span, where the bullet can be shot at only specified time moments. The duelist benefits from shooting as late as possible, but only when the duelist shoots first.
Objective. The objective is to determine optimal behavior of the duelists for a pattern of the duel discrete progression, by which the tension builds up as the duel end approaches and there are more possibilities to shoot.
Methods. Both the duelists act within the same conditions, and so the one-bullet silent duel is symmetric. Therefore, its optimal value is 0 and the duelists have the same optimal strategies. The shooting accuracy is linear being determined by an accuracy proportionality factor.
Results. Depending on the factor, all pure strategy solutions are found for such duels, whose possible-shooting moments comprise a progression pattern. According to this pattern, every next possible-shooting moment is obtained by adding the third of the remaining span to the current moment. The solutions for this pattern are compared to the known solutions for the geometrical-progression pattern and the pattern whose possible-shooting moments progress in a smoother manner.
Conclusions. The proved assertions contribute another specificity of the progressing-by-one-third shooting moments in linear-accuracy one-bullet silent duels to the games of timing. Compared to duels for other duel discrete progression patterns, the specificity consists in that the duel with progressing-by-one-third shooting moments has a constant interval of lower (weaker) shooting accuracies, at which the duelist possesses an optimal pure strategy. This interval is that symmetrically breaks the low-accuracy interval .
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