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Further on Potential Differential Games and Its Applications in Multi-leader Multi-follower Differential Games

Author

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  • Asmamaw Msgan Ayele

    (Addis Ababa University, Department of Mathematics)

  • Addis Belete Zewde

    (Dire Dawa University, Department of Mathematics)

  • Semu Mitiku Kassa

    (Botswana International University of Science and Technology P/Bag 16, Department of Mathematics and Statistical Sciences)

Abstract

The problem of obtaining Nash equilibria for non-cooperative differential games has been challenging, specially when the problem definition contains general nonseparable terms. In this paper, we present a more general set of sufficient conditions for the existence of potential functions for non-cooperative open-loop differential games. Moreover, potential differential game formulations are used to propose a solution approach for multi-leader multi-follower (MLMF) open-loop differential games. In the procedure, MLMF open-loop differential games are transformed into bi-level open-loop optimal control problems, whose solutions are Stackelberg-Nash equilibria of the original differential game.

Suggested Citation

  • Asmamaw Msgan Ayele & Addis Belete Zewde & Semu Mitiku Kassa, 2026. "Further on Potential Differential Games and Its Applications in Multi-leader Multi-follower Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-31, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02902-2
    DOI: 10.1007/s10957-025-02902-2
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