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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年12月16日

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  • Asmamaw Msgan Ayele,
  • Addis Belete Zewde,
  • Semu Mitiku Kassa

摘要

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.