Network games with dynamic players: Stabilization and output convergence to Nash equilibrium

Abstract

This paper addresses a class of network games played by dynamic agents using their outputs. Unlike most existing related works, the Nash equilibrium in this work is defined by functions of agent outputs instead of full agent states, which allows the agents to have more general and heterogeneous dynamics and maintain some privacy of their local states. The concerned network game is formulated with agents modeled by uncertain linear systems subject to external disturbances. The cost function of each agent is a linear quadratic function depending on the outputs of its own and its neighbors in the underlying graph. The main challenge stemming from this game formulation is that merely driving the agent outputs to the Nash equilibrium does not guarantee the stability of the agent dynamics. Using local output and the outputs from the neighbors of each agent, we aim at designing game strategies that achieve output Nash equilibrium seeking and stabilization of the closed-loop dynamics. Particularly, when each agents knows how the actions of its neighbors affect its cost function, a game strategy is developed for network games with digraph topology. When each agent is also allowed to exchange part of its compensator state, a distributed strategy can be designed for networks with connected undirected graphs or connected digraphs.

An inexact-penalty method for GNE seeking in games with dynamic agents

“…Let x * = π(y * ). By Assumption 3 and (9), f (π(y * )) − G(F (y * ) + ∇φ(y * )) = 0 (28) therefore x * = π(y * ) is an equilibrium point of (3). Now suppose there is another equilibrium x, we have 0 = f (x) − G(F (ȳ) + ∇φ(ȳ))…”

“…Any GNE seeking agorithm that is applied in these scenarios must deal with these two issues. Recently, NE seeking with partial-decision information has been considered for networks of dynamic agents (multi-integrator, LTI) [3]- [4], but most existing results are restricted to games with decoupled constraints. Considering games with coupled constraints, results exist for integrator agents, e.g., [5] in discrete-time and [6]- [7] in continuous-time and for multi-integrator agents in continuous-time [8].…”