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Dynamic spectrum access has become a promising approach that can coordinate different users' access to adapt to spectrum dynamics to improve spectrum efficiency. However, users competing for an open spectrum may have no incentive to cooperate with each other, and they may even exchange false private information about their channel conditions in order to get more access to the spectrum. Therefore, in this paper, we propose a self-enforcing truth-telling mechanism by modeling the distributed spectrum access as a repeated game. In this game, if any greedy user deviates from cooperation, punishment will be triggered. Through the Bayesian mechanism design, users have no incentive to reveal false channel conditions, and the competing users are enforced to cooperate with each other honestly. The simulation results show that the proposed scheme can greatly improve the spectrum efficiency by alleviating mutual interference; furthermore, the best strategy for each user is demonstrated to be reporting the actual channel condition.