Distributed energy resources (DERs) are deployed vastly to reduce carbon emission, improve power quality and maintain the reliability of distribution systems. With the introduction of new players, such as prosumers, which are constructed with DERs, distribution system operators (DSOs) are facing changes in the retail electricity market. Prosumers need a well-defined strategic bidding mechanism to maximize their operation revenue, while DSOs need a new market clearing mechanism for the changed retail electricity market. Thus, an innovative game-theoretic market framework for a prosumer-centric retail electricity market is proposed. A bilevel algorithm is adopted to model new features of DSOs, utility companies and prosumers. The supply function equilibrium model, Nikaido–Isoda functions, and relaxation algorithms are applied to analyse the competition among key participants in a retail electricity market. Extensive simulation results are employed to illustrate and validate the effectiveness of the proposed framework for bidding strategies of prosumers with a retail electricity market. Specifically, the strategy with dumping-bid or abnormal-bid from a prosumer is suppressed by the market operator in the model. Moreover, the sensitivity analysis shows that the proposed framework can handle various numbers of prosumers in the retail electricity market with reasonable computational time and convergence rate.