This paper proposes a novel game-theoretic model for peer-to-peer (P2P) energy trading among the prosumers in a community. The buyers can adjust the energy consumption behavior based on the price and quantity of the energy offered by the sellers. There exist two separate competitions during the trading process: (i) price competition among the sellers and (ii) seller selection competition among the buyers. The price competition among the sellers is modeled as a non-cooperative game. The evolutionary game theory is used to model the dynamics of the buyers for selecting sellers. Moreover, an M-leader and N-follower Stackelberg game approach is used to model the interaction between buyers and sellers. Two iterative algorithms are proposed for the implementation of the games such that an equilibrium state exists in each of the games. The proposed method is applied to a small community microgrid with photovoltaic (PV) and energy storage systems. Simulation results show the convergence of the algorithms and the effectiveness of the proposed model to handle the P2P energy trading. The results also show that P2P energy trading provides significant financial and technical benefits to the community and it is emerging as an alternative of cost-intensive energy storage systems.