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In this paper, spectrum access in cognitive radio networks is modeled as a repeated auction game subject to monitoring and entry costs. For secondary users, sensing costs are incurred as the result of primary users' activity. Furthermore, each secondary user pays the cost of transmission upon successful bidding for a channel. Knowledge regarding other secondary users' activity is limited due to the distributed nature of the network. The resulting formulation is thus a dynamic game with incomplete information. To solve such a problem, a Bayesian nonparametric belief update scheme is constructed based on the Dirichlet process. Efficient bidding learning algorithms are proposed via which users can decide whether or not to participate in the bidding according to the belief update. Properties of optimal bidding and initial bidding are proved. As demonstrated through extensive simulations, the proposed distributed scheme outperforms a myopic one-stage algorithm, and can achieve a good trade-off between long-term efficiency and fairness.