In this paper, we propose a two-tier evolutionary game for dynamic spectrum sharing using Licensed Shared Access (LSA) to serve the additional capacity needs of Mobile Network Operators (MNOs). The proposed algorithm ensures fair and demand-driven allocation of spectrum resources to LSA licensees, guaranteeing spectrum availability for licensees unlike previous spectrum sharing techniques. Moreover, we extend the evolutionary game by modeling the dynamic price adjustment strategies adopted by incumbents achieving an improved total gain for the incumbents. We prove the stability of the proposed evolutionary algorithm using Lyapunov stability criteria. Additionally, we perform simulations to prove convergence and stability of the evolutionary algorithm, and highlight the effects of dynamic parameters offered by incumbents such as price on overall average licensee payoff.