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Throughout this study, an adaptive competitive second-price pay-to-bid sealed auction game is presented as a solution to the fairness problem of spectrum sharing among a number of users in a cognitive radio environment. First, a comparison among three main spectrum-sharing game models; optimal, cooperative and competitive game models is discussed to highlight the advantages and disadvantages of each model. The results prove that cooperative games aim to achieve Nash equilibrium between primary and secondary players and provide better revenue to them. Also, it proves that cooperative games are best when the number of secondary users changes dynamically, but only when the number is low. As in practical situations, the number of secondary users might increase dramatically and cooperative games will lose their powerful advantage once that happens. As a result, the proposed mechanism creates a competition between the bidders and offers better revenue to all players in terms of fairness. The proposed model ensures that users with better channel quality, higher traffic priority and fairer bids will get a better chance to share the offered spectrum. It is shown by numerical results that the proposed mechanism could reach the maximum total profit for all users with better fairness.