Prescribed-time multi-coalition Nash equilibrium seeking by event-triggered communication

This article investigates the event-triggered prescribed-time Nash equilibrium seeking problem among multiple coalitions of agents in noncooperative games. Each coalition acts as a virtual player in the noncooperative game, with decisions made by its member agents. Agents lack complete information about others' decisions and instead estimate them through a communication graph. An event-triggered prescribed-time multi-coalition Nash equilibrium seeking method is developed based on the leader-following consensus protocol, dynamic average consensus protocol, and gradient play. This method ensures the Nash equilibrium of the multi-coalition game is reached within a prescribed time, even when communication between agents only occurs under specific triggering conditions-effectively conserving communication resources. Unlike existing approaches, the proposed algorithm allows precise settling time assignment without prior knowledge of system parameters. This algorithm also prevents Zeno behavior. Lastly, the efficiency of the designed algorithm is demonstrated through simulation experiments.