Zero-sum Games on a Product of Staircase-Function Finite Spaces

Romanuke, Vadim

doi:10.7862/rf.2021.6

Cited by 1 publication

(2 citation statements)

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“…Games of timing include several distinct types of duels [4,8,13]. Silent duels constitute a wide class of these games [8,15,1].…”

Section: Introductionmentioning

confidence: 99%

“…Games of timing include several distinct types of duels [4,8,13]. Silent duels constitute a wide class of these games [8,15,1]. In a typical silent duel, which alternatively may be called noiseless, each of two players has exactly one bullet, and it is unknown to them whether a bullet was red or not until the end of the duel time span [11,3].…”

Section: Introductionmentioning

confidence: 99%

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Pure strategy saddle point in progressive discrete silent duel with quadratic accuracy functions of the players Vadim Romanuke

Romanuke

2023

VAM

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A zero-sum game dened on a nite subset of the unit square is considered. The game is a progressive discrete silent duel, in which the kernel is skew-symmetric. As the duel starts, time moments of possible shooting become denser by a geometric progression. Apart from the duel beginning and end moments, every following 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. It is proved that the solution of a progressive discrete silent duel, with identical accuracy functions of the duelists, is a pure strategy saddle point. For nontrivial games, where the duelist possesses more than just one moment of possible shooting between the duel beginning and end moments, the saddle point is single. Moreover, the solution renders the game into an invariant decision. For the linear accuracy, whose value is not less than its time moment, the optimal strategy is the middle of the duel time span. For the quadratic accuracy the optimal strategy is the middle of the second half of the duel time span. If the linear accuracy value is less than its time moment, the middle of the duel time span is never optimal.

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“…Games of timing include several distinct types of duels [4,8,13]. Silent duels constitute a wide class of these games [8,15,1].…”

Section: Introductionmentioning

confidence: 99%