The effect of collusion games on the profit of primary networks and secondary heterogeneous cognitive radio networks with femtocells

This paper studies the effect of the different pricing games played by the primary user (PU) operators on the profit of both the PU networks and the cognitive base station (CBS). We show that the price achieved by the PU operators in the collusion game (called the Pareto point) is the maximum price that can be achieved in the competitive game when the substitutability parameter is higher than zero. However, for negative values of the substitutability parameter, the Pareto point represents the minimum price that can be offered by the PU operators. Moreover, the effect of the collusion game on the profit of the CBS has also been investigated, and the simulations show that the worst case for the CBS in terms of profit is not associated with the highest price that can be offered by the PU networks.