Distributed Nash equilibrium computation in aggregative games: An event-triggered algorithm

This paper is concerned with the problem of distributed Nash equilibrium computation in aggregative games. Note that the traditional computation algorithms are designed based on time-scheduled communication strategy, which may lead to high communication consumption of the whole network. To reduce the consumption, this paper proposes a novel distributed algorithm with an event-triggered mechanism, where the communication between any two agents is only carried out when an edge-based event condition is triggered. In the convergence analysis of the proposed algorithm, an important event-related error variable is firstly defined. Then, based on a zero-sum property of this event-related error, two key relations on the agents' estimates in the proposed algorithm are provided. Further, by using these relations, it is proven that the agents' estimates can achieve a Nash equilibrium under a proper event-triggering condition. Finally, examples on the demand response of power systems are presented to verify the theoretical findings. (C) 2019 Elsevier Inc. All rights reserved.