Dynamic spectrum access (DSA) can effectively improve the spectrum efficiency and alleviate the spectrumscarcity, by allowing unlicensed secondary users (SUs) to access the licensed spectrumof primary users (PUs) opportunistically. Cooperative spectrum sharing is a new promising paradigm to provide necessary incentives for both PUs and SUs in dynamic spectrum access. The key idea is that SUs relay the traffic of PUs in exchange for the access time on the PUs’ licensed spectrum. In this paper, we formulate the cooperative spectrum sharing between multiple PUs and multiple SUs as a two-sided market, and study the market equilibrium under both complete and incomplete information. First, we characterize the sufficient and necessary conditions for the market equilibrium. We analytically show that there may exist multiple market equilibria, among which there is always a unique Pareto-optimal equilibrium for Pus (called PU-Optimal-EQ), in which every PU achieves a utility no worse than in any other equilibrium. Then, we show that under complete information, the unique Pareto-optimal equilibrium PU-Optimal-EQ can always be achieved despite the competition among PUs; whereas, under incomplete information, the PU-Optimal-EQ may not be achieved due to the mis-representations of SUs (in reporting their private information). Regarding this, we further study the worse-case equilibrium for PUs, and characterize a Robust equilibrium for PUs (called PU-Robust-EQ), which provides every PU a guaranteed utility under all possible mis-representation behaviors of SUs. Numerical results show that in a typical network where the number of PUs and SUs are different, the performance gap between PU-Optimal-EQ and PU-Robust-EQ is quite small (e.g., less than 10 percent in the simulations).