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An integrated view of energy markets has led to the introduction of new market participants named energy retailers (ERs). Competition among ERs in an integrated market greatly improves market performance in areas such as sustainability, supply security, and environmental awareness. ER performance is evaluated in an integrated market with emission penalty reduction in the objective function. Bi-level programming is used to model an ER game, and the equilibria of different configurations are compared. In the game's first level, ERs offer various energy carrier selling prices to optimise profits. In the second level, consumers respond by switching from the retail market to minimise their energy bills. This complex problem is simplified utilising a discretisation method based on Nash theory. The configuration scenarios include different structures, components, and ER-user transactions. The effectiveness of the proposed configuration scenarios is validated by their implementation in an illustrative case study. Energy retailers purchase energy from various sources including bilateral contracts with energy suppliers, wholesale market participation, and self-generation. Electricity retailers explicitly represent the difficulties of energy procurement and bidding strategies. Simulation results for the proposed energy system model indicate better performance than that of the base case and a noticeable increment in retailer profit. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.