An increasing number of vehicles make spectrum resources face serious challenges in vehicular cognitive small-cell networks. The\nmeans of spectrum sharing can greatly alleviate this pressure. In this paper, we introduce a supermodular game theoretic approach\nto analyze the problem of spectrum sharing. The small-cell BS (primary service provider, PSP) and the vehicle (secondary service\nprovider, SSP) can share the spectrum, where the PSP can sell idle spectrum resources to the SSP. This is taken as a spectrum\ntrading market, and a Bertrand competition model is considered to depict this phenomenon. Different PSPs compete with each\nother to maximize their individual profits. The Bertrand competition model can be proved as a supermodular game, and the\ncorresponding Nash equilibrium (NE) solution is provided as the optimal price solution. Hence, an improved genetic simulated\nannealing algorithm is designed to achieve NE. Simulation results demonstrate that the NE point for the price of the primary\nservice provider exists. The change of the exogenous variable is also analyzed on the equilibrium point.
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