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Pure Strategy Solutions in the Progressive Discrete Silent Duel with Identical Linear Accuracy Functions and Shooting Uniform Jitter

Romanuke Vadim

Journal of Mathematics and Applications

2024

Vol. 47

91--108

The progressive discrete silent duel is studied modeling limited observability within a system in order to make the best discretetime decision. The moments to make a decision (to take an action, to shoot a bullet) are scheduled beforehand. The kernel of the duel is skew-symmetric, and the duelists (players) have identical linear accuracy functions. The duel is a finite zero-sum game defined on a subset of the unit square. As the duel starts, time moments of possible shooting become denser by a geometric progression. Apart from the duel beginning and end time moments, every following time moment is the partial sum of the respective geometric series, to which a value of the jitter is added. Regardless of the jitter, both the duelists have the same optimal strategies and the game optimal value is 0 due to the skew-symmetry. The only optimal behavior of the duelist at any positive jitter is to shoot at the positively jittered middle of the duel time span.