Hybrid Nash Equilibrium Seeking Under Partial-Decision Information: An Adaptive Dynamic Event-Triggered Approach

This article is concerned with the hybridNash equilibrium (NE) seeking problem over a network in a partial-decision information scenario. Each agent has access to both its own cost function and local decision information of its neighbors. First, an adaptive gradient-based algorithm is constructed in a fully distributed manner with the guaranteed convergence to the NE, where the network communication is required. Second, in order to save communication cost, a novel event-triggered scheme, namely, edge-based adaptive dynamic event-triggered (E-ADET) scheme, is proposed with online-tuned triggering parameter and threshold, and such a scheme is proven to be fully distributed and free of Zeno behavior. Then, a hybrid NE seeking algorithm, which is also fully distributed, is constructed under the E-ADET scheme. By means of the Lipschitz continuity and the strong monotonicity of the pseudogradient mapping, we show the convergence of the proposed algorithms to the NE. Compared with the existing distributed algorithms, our algorithms remove the requirement on global information, thereby exhibiting the merits of both flexibility and scalability. Finally, two examples are provided to validate the proposed NE seeking methods.

Automated summary

This article focuses on the problem of hybrid Nash equilibrium seeking over a network in a partial-decision information scenario. A fully distributed adaptive gradient-based algorithm is constructed with guaranteed convergence to the equilibrium. To save communication cost, a novel event-triggered scheme called edge-based adaptive dynamic event-triggered (E-ADET) scheme is proposed, which is proven to be fully distributed and free of Zeno behavior. Furthermore, a fully distributed hybrid equilibrium seeking algorithm is constructed under the E-ADET scheme, with convergence guaranteed by utilizing the Lipschitz continuity and the strong monotonicity of the pseudogradient mapping.