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

• Autorzy: Romanuke Vadim

Identyfikatory

DOI

10.7862/rf.2024.6

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

game of timing; silent duel; linear accuracy function; Matrix game; pure strategy solution; jittered possible shooting moments

PL

gra na czas; cichy pojedynek; funkcja dokładności liniowej; gra Matrix; czyste rozwiązanie strategiczne; roztrzęsione możliwe momenty fotografowania

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2024
• Tom: Vol. 47
• Strony: 91--108
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Romanuke Vadim

• Faculty of Mechanical and Electrical Engineering, Polish Naval Academy, Gdynia, Poland

• https://orcid.org/000-0003-3543-3087

Bibliografia

• [1] E.N. Barron, Game Theory : An Introduction (2nd ed.), Wiley, Hoboken, New Jersey, 2013.
• [2] R.A. Epstein, The Theory of Gambling and Statistical Logic (2nd ed.), Academic Press, Burlington, Massachusetts, 2013.
• [3] S. Karlin, The Theory of Infinite Games. Mathematical Methods and Theory in Games, Programming, and Economics, Pergamon, London — Paris, 1959.
• [4] J.P. Lang, G. Kimeldorf, Duels with continuous firing, Management Science 2(4) (1975) 470 — 476.
• [5] M.J. Osborne, An Introduction to Game Theory, Oxford University Press, Oxford, UK, 2003.
• [6] J.F. Reinganum, Chapter 14 — The Timing of Innovation: Research, Development, and Diffusion, in: R. Willig, R. Schmalensee (Eds.), Handbook of Industrial Organization, Elsevier, North-Holland, Volume 1, 1989, pp. 849 — 908.
• [7] V.V. Romanuke, Theory of Antagonistic Games, New World — 2000, Lviv, 2010.
• [8] V.V. Romanuke, Fast solution of the discrete noiseless duel with the nonlinear scale on the linear accuracy functions, Herald of Khmelnytskyi National University. Economical Sciences 5 (4) (2010) 61 — 66.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).