With the high penetration of renewable energy resources, energy prosumers and microgrids can trade energy directly with each other in a hierarchical way. This paper develops a nested market clearing algorithm that alternately produces optimal trading results in both inter- and intra-microgrid markets. The inter-microgrid market refers to the energy exchange among microgrids in distribution network. The intra-microgrid market is the energy sharing among prosumers inside microgrids. We use a distributionally robust optimization approach that is based on prospect theory (PT) to account for the complexity of prosumers’ behavior. The prosumers’ irrational behavior refers to the incomplete rationality in the market. The objective uncertainty and risk preference inside microgrids are modeled uniformly, based on which the alternating direction multiplier method (ADMM) algorithm is employed to solve this problem while preserving privacy. By filtering the marginal energy prosumers in each microgrid, the privacy of microgrids in the inter-microgrid market is preserved as well. Moreover, we prove that the proposed nested market clearing algorithm can reach the global Nash equilibrium. Numerical simulations demonstrate that the condensed equilibrium representation (CER) successfully selects energy prosumers from an intra-microgrid market to participate in an inter-microgrid market. The impact of risk preference parameters on the total utility is also analyzed.