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

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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 \( \upalpha \)-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.

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their helpful comments for revising the article.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

    El-Saeed Ammar

  2. Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, 41522, Ismailia, Egypt

    M. G. Brikaa

  3. Department of Mathematics Faculty of Science, Suez Canal University, 41522, Ismailia, Egypt

    Entsar Abdel-Rehim

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  1. El-Saeed Ammar
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  2. M. G. Brikaa
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  3. Entsar Abdel-Rehim
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Correspondence to M. G. Brikaa.

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Ammar, ES., Brikaa, M.G. & Abdel-Rehim, E. A study on two-person zero-sum rough interval continuous differential games. OPSEARCH 56, 689–716 (2019). https://doi.org/10.1007/s12597-019-00383-2

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