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In this paper, we model the various users in a wireless network (e.g., cognitive radio network) as a collection of selfish autonomous agents that strategically interact to acquire dynamically available spectrum opportunities. Our main focus is on developing solutions for wireless users to successfully compete with each other for the limited and time-varying spectrum opportunities, given experienced dynamics in the wireless network. To analyze the interactions among users given the environment disturbance, we propose a stochastic game framework for modeling how the competition among users for spectrum opportunities evolves over time. At each stage of the stochastic game, a central spectrum moderator (CSM) auctions the available resources, and the users strategically bid for the required resources. The joint bid actions affect the resource allocation and, hence, the rewards and future strategies of all users. Based on the observed resource allocations and corresponding rewards, we propose a best-response learning algorithm that can be deployed by wireless users to improve their bidding policy at each stage. The simulation results show that by deploying the proposed best-response learning algorithm, the wireless users can significantly improve their own bidding strategies and, hence, their performance in terms of both the application quality and the incurred cost for the used resources.