Distributed Nash Equilibrium Seeking in Multiagent Games Under Switching Communication Topologies

This paper investigates distributed Nash equilibrium seeking in multiagent games under switching communication topologies. To be specific, the communication topology is supposed to be switching among a set of strongly connected digraphs, which might suffer from occasional loss of communication due to sensor failure, packet loss, etc. The synthesis of the leader-following consensus protocol and the gradient play is exploited to achieve the distributed Nash equilibrium seeking under the switching communication topologies. Switching topology without loss of communication is firstly considered, followed by switching topology subject to missing communication within some time slots. For both situations, nonquadratic and quadratic games are addressed separately. Local convergence results are presented for nonquadratic games and nonlocal convergence results are provided for quadratic games. The theoretical results are verified by numerical examples.

I. Introduction

The penetration of game theoretical analyses into cooperative control and optimization of multiagent systems (see [1]–[4]) motivates the researchers to investigate games on communication graphs [5]–[12]. Aggregative games, in which the players’ payoff functions depend on its own action and an aggregate of all the players’ actions, were considered in [5] and [6] and general multiagent games were explored in [7] and [8]. Gossip-based algorithms were studied in [5] and [7] and consensus-based algorithms were developed in [6] and [8]. A modified fictitious play algorithm was studied in [9] and [10] for a special class of multiagent games under preassigned communication graphs. Two-network zero-sum games were considered in [11] under undirected graphs and weight-balanced digraphs. The two-network zero-sum game is composite of two networks acting as virtual players in a two-player zero-sum game. Nevertheless, the “networks ” are not the actual decision-makers and their actions are determined by the agents in the networks. The two-network zero-sum game was further investigated by Lou et al. [12] under switching communication topologies.