  It is known that the capacity of the intelligent reflecting surface (IRS)
aided cellular network can be effectively improved by reflecting the incident
signals from the transmitter in a low-cost passive reflecting way. In this
paper, we study the adoption of an IRS for downlink multi-user communication
from a multi-antenna base station (BS). Nevertheless, in the actual network
operation, the IRS operator can be selfish or have its own objectives due to
competing/limited resources as well as deployment/maintenance cost. Therefore,
in this paper, we develop a Stackelbeg game model to analyze the interaction
between the BS and the IRS operator. Specifically, different from the existing
studies on IRS that merely focus on tuning the reflection coefficient of all
the reflection elements, we consider the reflection resource (elements)
management, which can be realized via trigger module selection under our
proposed IRS architecture that all the reflection elements are partially
controlled by independent switches of controller. A Stackelberg game-based
alternating direction method of multipliers (ADMM) is proposed to jointly
optimize the transmit beamforming at the BS and the passive beamforming of the
triggered reflection modules. Numerical examples are presented to verify the
proposed studies. It is shown that the proposed scheme is effective in the
utilities of both the BS and IRS.
