Abstract
The authors solve the competition problem for two enterprises. The problem reduces to an antagonistic dynamic game on a fixed time interval with a convex compact objective set. The problem is solved in the interests of one enterprise. The set of initial positions is constructed, for which an enterprise necessarily attains the objective at a given finite instant of time under the worst behavior of the competitive enterprise.
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REFERENCES
R. Isaaks (1967) Differential Games Mir Moscow
L. S. Pontryagin (1980) ArticleTitleLinear differential games of pursuit Mat. Sb. 112 307–330
N. N. Krasovskii (1985) Control of a Dynamic System. The Problem on a Minimum of a Guaranteed Result Nauka Moscow
B. N. Pshenichnyi (1969) ArticleTitleDifferential games structure Dokl. AN SSSR 184 IssueID2 285–287
B. N. Pshenichnyi and M. I. Sagaidak, “Differential games with fixed time,” Kibernetika, No. 2, 54–63 (1970).
B. N. Pshenichnyi (1980) Convex Analysis and Extreme Problems Nauka Moscow
E. S. Polovinkin (1986) Elements of the Multivalued Mappings Theory: A Manual MFTI Moscow
R. V. Konstantinov (2001) ArticleTitleOn a quasilinear differential game of pursuit with a simple dynamics under a phase constraint Mat. Zametki 69 IssueID4 581–590
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The study was supported from the RFFI (grant No. 01-01-00743).
Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 108–115, September–October 2004.
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Konstantinov, R.V., Polovinkin, E.S. Mathematical simulation of a dynamic game in the enterprise competition problem. Cybern Syst Anal 40, 720–725 (2004). https://doi.org/10.1007/s10559-005-0009-8
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DOI: https://doi.org/10.1007/s10559-005-0009-8