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It is known that the capacity of the intelligent reflecting surface (IRS)aided cellular network can be effectively improved by reflecting the incidentsignals from the transmitter in a low-cost passive reflecting way.Nevertheless, in the actual network operation, the base station (BS) and IRSmay belong to different operators, consequently, the IRS is reluctant to helpthe BS without any payment. Therefore, this paper investigates price-basedreflection resource (elements) allocation strategies for an IRS-aided multiusermultiple-input and single-output (MISO) downlink communication systems, inwhich all transmissions over the same frequency band. Assuming that the IRS iscomposed with multiple modules, each of which is attached with a smartcontroller, thus, the states (active/idle) of module can be operated by itscontroller, and all controllers can be communicated with each other via fiberlinks. A Stackelberg game-based alternating direction method of multipliers(ADMM) is proposed to jointly optimize the transmit beamforming at the BS andthe passive beamforming of the active modules. Numerical examples are presentedto verify the proposed algorithm. It is shown that the proposed scheme iseffective in the utilities of both the BS and IRS.

A Stackelberg Game Approach to Resource Allocation for IRS-aided Communications