In this paper, we establish a game theoretic framework of the auction based dynamic spectrum access for multitype buyers (i.e., the secondary users that have different risk preferences) in cognitive radio networks where the auction mechanisms of the primary user are parameterized and can be adaptively designed. We design the utility functions of the multitype secondary users. The proposed game is a discrete game having at least one mixed or pure strategy Nash equilibrium. Based on the concept of learning automata, we propose a distributed algorithm to learn the Nash equilibrium of the proposed game with limited feedback information and prove its convergence to the Nash equilibrium of our proposed game with properly designed utility function. Simulation results show that our proposed algorithm is efficient and can achieve much higher performance than the traditional fixed auction mechanism schemes and the random algorithm.