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

Stanisław Trybuła

Applicationes Mathematicae (1993)

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

Abstract

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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.

How to cite

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Trybuła, 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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  1. [1] A. Cegielski, Tactical problems involving uncertain actions, J. Optim. Theory Appl. 49 (1986), 81-105 Zbl0568.90101
  2. [2] A. Cegielski, Game of timing with uncertain number of shots, Math. Japon. 31 (1986), 503-532 Zbl0627.90098
  3. [3] M. Fox and G. Kimeldorf, Noisy duels, SIAM J. Appl. Math. 19 (1969), 353-361 Zbl0172.44801
  4. [4] S. Karlin, Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 2, Addison-Wesley, Reading, Mass., 1959 
  5. [5] G. Kimeldorf, Duels: an overview, in: Mathematics of Conflict, North-Holland, 1983, 55-71 Zbl0573.90105
  6. [6] K. Orłowski and T. Radzik, Discrete silent duels with complete counteraction, Optimization 16 (1985), 419-429 Zbl0571.90100
  7. [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. [8] A. Styszyński, An n-silent-vs.-noisy duel with arbitrary accuracy functions, Zastos. Mat. 14 (1974), 205-225 
  9. [9] Y. Teraoka, Noisy duels with uncertain existence of the shot, Internat. J. Game Theory 5 (1976), 239-250 
  10. [10] Y. Teraoka, A single bullet duel with uncertain information available to the duelists, Bull. Math. Statist. 18 (1979), 69-80 Zbl0424.90087
  11. [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. [12] S. Trybuła, Solution of a silent duel under general assumptions, Optimization 22 (1991), 449-459 Zbl0746.90098
  13. [13] S. Trybuła, A mixed duel under arbitrary motion, Applicationes Math., to appear Zbl0833.90149
  14. [14] S. Trybuła, A silent versus partially noisy one-bullet duel under arbitrary motion, ibid., to appear Zbl0793.90112
  15. [15] N. N. Vorob'ev, Foundations of the Theory of Games. Uncoalition Games, Nauka, Moscow, 1984 (in Russian) 

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