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Developing the electricity market at the distribution level can facilitate the energy transactions in distribution networks with a high penetration level of distributed energy resources (DERs) and microgrids (MGs). However, the lack of comprehensive information about the marginal production cost of competitors leads to uncertainties in the optimal bidding strategy of participants. The electricity demand within the network and the price in the wholesale electricity market are two other sources of the uncertainties. In this paper, a day-ahead-market-based framework for managing the energy transactions among MGs and other participants in distribution networks is introduced. A game-theory-based method is presented to model the competition and determine the optimal bidding strategy of participants in the market. Robust optimization technique is employed to capture the uncertainties in the marginal cost of competitors. Additionally, the uncertainties in demand are modeled using a scenario-based stochastic approach. The results obtained from case studies reveal the merit of considering competition modeling and uncertainties.