The traditional spectrum auctions require a central auctioneer. Then, the secondary users (SUs) can bid for spectrum in multiple auction or sealed auction way. In this paper, we address the problem of distributed spectrum sharing in the cognitive networks where multiple owners sell their spare bands to multiple SUs. Each SU equips multi-interface/multi-radio, so that SU can buy spare bands from multiple owners. On the other hand, each owner can sell its spare bands to serval SUs. There are two questions to be addressed for such an environment: the first one is how to select bands/the owners for each SU; the second one is how to decide the competitive prices for the multiple owners and multiple SUs. To this end, we propose a two-side multi-band market game theoretic framework to jointly consider the benefits of all SUs and owners. The equilibrium concept in such games is named core. The outcomes in the core of the game cannot be improved upon by any subset of players. These outcomes correspond exactly to the price-lists that competitively balance the benefits of all SUs and owners. We show that the core in our model is always non-empty. When the measurement of price takes discrete value, the core of the game is defined as discrete core. The Dynamic Multi-band Sharing algorithm (DMS) is proposed to converge to the discrete core of the game. With small enough measurement unit of price, the algorithm can achieve the optimal performance compared with centralized one in terms of the system utility.