  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.
Nevertheless, in the actual network operation, the base station (BS) and IRS
may belong to different operators, consequently, the IRS is reluctant to help
the BS without any payment. Therefore, this paper investigates price-based
reflection resource (elements) allocation strategies for an IRS-aided multiuser
multiple-input and single-output (MISO) downlink communication systems, in
which all transmissions over the same frequency band. Assuming that the IRS is
composed with multiple modules, each of which is attached with a smart
controller, thus, the states (active/idle) of module can be operated by its
controller, and all controllers can be communicated with each other via fiber
links. 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 active modules. Numerical examples are presented
to verify the proposed algorithm. It is shown that the proposed scheme is
effective in the utilities of both the BS and IRS.
