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

Author

Listed:
  • El-Saeed Ammar

    (Tanta University)

  • M. G. Brikaa

    (Suez Canal University)

  • Entsar Abdel-Rehim

    (Suez Canal University)

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.

Suggested Citation

  • El-Saeed Ammar & M. G. Brikaa & Entsar Abdel-Rehim, 2019. "A study on two-person zero-sum rough interval continuous differential games," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 689-716, September.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:3:d:10.1007_s12597-019-00383-2
    DOI: 10.1007/s12597-019-00383-2
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    References listed on IDEAS

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    Cited by:

    1. Gaurav Sharma & Sapan Kumar Das & Ganesh Kumar, 2023. "Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1456-1487, September.

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