Network Aggregative Game in Unknown Dynamic Environment With Myopic Agents and Delay

In this article, the framework of network aggregative game (NAG) is extended by considering the interaction of players in a dynamic environment whose model is not known to them. The cost function of each player depends on its own strategy, the aggregate strategy of its neighbor players in the network, and also the state of the environment. The state of the environment evolves with a dynamics that is affected by the strategies of players as an input to the model. The players of NAG are modeled as myopic selfish agents who observe the decision value of their neighbors and the state of the environment with some time delay and, then, adjust their decisions using a projected subgradient rule. The main contribution of this article is to provide conditions in which the strategies of myopic agents converge to the unique fixed-point Nash equilibrium point of the proposed dynamic NAG. Furthermore, as a case study, the framework is applied to a wireless network by modeling the service providers as the agents and evolution of service selection by users as the dynamics of the environment.

I. Introduction

Network games have been gaining importance among researchers in recent years [1]. In the network game framework, the cost function of each individual agent is influenced by other neighboring agents via a communication network. Each agent aims to find its optimal decision selfishly while communicating with its neighbors [2]. In particular, when the cost function of an agent is affected by an aggregation (e.g., weighted sum) of its neighbors’ decisions, the problem is called network aggregative game (NAG). The NAG framework can be applied to a variety of applications, such as social networks [3], wireless cellular networks [4], public good provision [5], and microgrids [6].