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We consider a dynamic spectrum access scenario in which transmission opportunities are allocated to users based on a second price, sealed bid auction. Each user experiences a time-varying channel and submits a bid for transmission right in each time slot. A base station collects bids from all users and allocates the channel to a user with the highest bid, who then pays the price equal the second highest bid. The distinctive feature of our model is that it treats time as money and allows each user to bid and to pay for the transmission rights using his/her own communication time. For each time slot, the value of a bid submitted by each user is equal the amount of time he/she promises to forfeit to the base station for the right to transmit during the remaining of the time slot. That means the base station collects part of each time slot from the winning user for its own usage and allocates the rest to the winning user. Users can vary their bids based on their channel conditions, subject to constraints on average budgets. From the users' point of view, we show that there exists Nash equilibrium bidding strategies in the two-user case. From the base station's point of view, we investigate how average budget constraints should be set to balance between base station's revenue and users' satisfaction.