A mixed duel under arbitrary motion and uncertain existence of the shot

• Autorzy: Stanisław Trybuła
• Języki publikacji: EN

Abstrakty

EN

The purpose of the paper is to solve a mixed duel in which the numbers of shots given to the players are independent 0-1-valued random variables. The players know their distributions as well as the accuracy function P, the same for both players. It is assumed that the players can move as they like and that the maximal speed of the first player is greater than that of the second player. It is shown that the game has a value, and a pair of optimal strategies is found.

Słowa kluczowe

EN

zero-sum game; mixed duel; game of timing

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 1
• Strony: 39-44

Daty

wydano

1993

otrzymano

1992-8-5

Twórcy

autor

Stanisław Trybuła

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [1] A. Cegielski, Tactical problems involving uncertain actions, J. Optim. Theory Appl. 49 (1986), 81-105
• [2] A. Cegielski, Game of timing with uncertain number of shots, Math. Japon. 31 (1986), 503-532
• [3] M. Fox and G. Kimeldorf, Noisy duels, SIAM J. Appl. Math. 19 (1969), 353-361
• [4] S. Karlin, Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 2, Addison-Wesley, Reading, Mass., 1959
• [5] G. Kimeldorf, Duels: an overview, in: Mathematics of Conflict, North-Holland, 1983, 55-71
• [6] K. Orłowski and T. Radzik, Discrete silent duels with complete counteraction, Optimization 16 (1985), 419-429
• [7] R. Restrepo, Tactical problems involving several actions, in: Contributions to the Theory of Games, Vol III, Ann. of Math. Stud. 39, Princeton Univ. Press, 1957, 313-335
• [8] A. Styszyński, An n-silent-vs.-noisy duel with arbitrary accuracy functions, Zastos. Mat. 14 (1974), 205-225
• [9] Y. Teraoka, Noisy duels with uncertain existence of the shot, Internat. J. Game Theory 5 (1976), 239-250
• [10] Y. Teraoka, A single bullet duel with uncertain information available to the duelists, Bull. Math. Statist. 18 (1979), 69-80
• [11] S. Trybuła, A noisy duel under arbitrary moving I-VI, Zastos. Mat. 20 (1990), 491-495, 497-516, 517-530; 21 (1991), 43-61, 63-81, 83-98
• [12] S. Trybuła, Solution of a silent duel under general assumptions, Optimization 22 (1991), 449-459
• [13] S. Trybuła, A mixed duel under arbitrary motion, Applicationes Math., to appear
• [14] S. Trybuła, A silent versus partially noisy one-bullet duel under arbitrary motion, ibid., to appear
• [15] N. N. Vorob'ev, Foundations of the Theory of Games. Uncoalition Games, Nauka, Moscow, 1984 (in Russian)