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

Applicationes Mathematicae (1993)

- Volume: 22, Issue: 1, page 39-44
- ISSN: 1233-7234

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topTrybuła, Stanisław. "A mixed duel under arbitrary motion and uncertain existence of the shot." Applicationes Mathematicae 22.1 (1993): 39-44. <http://eudml.org/doc/219081>.

@article{Trybuła1993,

abstract = {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.},

author = {Trybuła, Stanisław},

journal = {Applicationes Mathematicae},

keywords = {zero-sum game; mixed duel; game of timing; value; pair of optimal},

language = {eng},

number = {1},

pages = {39-44},

title = {A mixed duel under arbitrary motion and uncertain existence of the shot},

url = {http://eudml.org/doc/219081},

volume = {22},

year = {1993},

}

TY - JOUR

AU - Trybuła, Stanisław

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

JO - Applicationes Mathematicae

PY - 1993

VL - 22

IS - 1

SP - 39

EP - 44

AB - 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.

LA - eng

KW - zero-sum game; mixed duel; game of timing; value; pair of optimal

UR - http://eudml.org/doc/219081

ER -

## References

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- [2] A. Cegielski, Game of timing with uncertain number of shots, Math. Japon. 31 (1986), 503-532 Zbl0627.90098
- [3] M. Fox and G. Kimeldorf, Noisy duels, SIAM J. Appl. Math. 19 (1969), 353-361 Zbl0172.44801
- [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 Zbl0573.90105
- [6] K. Orłowski and T. Radzik, Discrete silent duels with complete counteraction, Optimization 16 (1985), 419-429 Zbl0571.90100
- [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 Zbl0078.33202
- [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 Zbl0424.90087
- [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 Zbl0772.90100
- [12] S. Trybuła, Solution of a silent duel under general assumptions, Optimization 22 (1991), 449-459 Zbl0746.90098
- [13] S. Trybuła, A mixed duel under arbitrary motion, Applicationes Math., to appear Zbl0833.90149
- [14] S. Trybuła, A silent versus partially noisy one-bullet duel under arbitrary motion, ibid., to appear Zbl0793.90112
- [15] N. N. Vorob'ev, Foundations of the Theory of Games. Uncoalition Games, Nauka, Moscow, 1984 (in Russian)

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