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Pure strategy solutions of the progressive discrete silent duel with generalized identical quadratic accuracy functions.
- Source :
-
Discrete Applied Mathematics . May2024, Vol. 349, p215-232. 18p. - Publication Year :
- 2024
-
Abstract
- A generalized class of the discrete game of timing is solved as a finite zero-sum game defined on a symmetric lattice of the unit square. The game is a progressive discrete silent duel whose kernel is skew-symmetric, and the players, referred to as duelists, have identical shooting accuracy functions featured with an accuracy proportionality factor a and a power constant β describing nonlinearity of the shooting accuracy. 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. Due to the skew-symmetry, both the duelists have the same optimal strategies and the game optimal value is 0. As the duelist has a single bullet, there is no reason for considering solutions in mixed strategies, if any, with non-singleton supports. If a ⩾ 2 β − 1 , the duelist's optimal strategy is the middle of the duel time span; otherwise, the duel solution may be not a pure strategy solution. The case of quadratic accuracy for β = 2 is further considered, which is reasoned by that linearly developing real-time processes are quite rare, and the quadratic accuracy is a non-linearity pattern that makes an interaction model more reliable by slightly diminishing the duelist's confidence. Thus, the case of a < 2 β − 1 is thoroughly studied for pure strategy solutions. A boundary case of a is found, by which the duel has four pure strategy solutions which are of the time moment preceding the duel end moment and the duel end moment itself. • Discrete game of timing is solved as a finite zero-sum game on a symmetric lattice. • Duelist is featured with shooting accuracy proportionality and nonlinearity factors. • The breaking point of the accuracy is found above which pure strategy solutions exist. • Pure strategy solutions are found below the breaking point for the quadratic accuracy. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ZERO sum games
*GEOMETRIC series
*STRATEGY games
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 349
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176247660
- Full Text :
- https://doi.org/10.1016/j.dam.2024.02.015