A study on two-person zero-sum rough interval continuous differential games

El-Saeed Ammar (), M. G. Brikaa () and Entsar Abdel-Rehim ()
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El-Saeed Ammar: Tanta University
M. G. Brikaa: Suez Canal University
Entsar Abdel-Rehim: Suez Canal University

OPSEARCH, 2019, vol. 56, issue 3, No 4, 689-716

Abstract: Abstract In this paper, we concentrate on solving the zero-sum two-person continuous differential games using rough programming approach. A new class defined as rough continuous differential games is resulted from the combination of rough programming and continuous differential games. An effective and simple technique is given for solving such problem. In addition, the trust measure and the expected value operator of rough interval are used to find the $$ \upalpha $$ α -trust and expected equilibrium strategies for the rough zero-sum two-person continuous differential games. Moreover, sufficient and necessary conditions for an open loop saddle point solution of rough continuous differential games are also derived. Finally, a numerical example is given to confirm the theoretical results.

Keywords: Two-person zero-sum game; Rough interval; Differential games; Trust measure; Sufficient and necessary conditions (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s12597-019-00383-2

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