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The global share of renewable energy sources (RES) in total generation capacity reached 34.7% in 2019 and has been continuously increasing. Power system flexibility addressing the uncertainty and variability of RES has become a major concern in energy transition. This paper proposes to apply mobile energy storage (MES) from independent MES owners as a flexibility-enhancement ancillary service in the day-ahead electricity market. First, we have proposed a market-based methodology to incent MES owners to provide flexibility service in power systems by simultaneously releasing Locational Marginal price (LMP) and Uncertainty Marginal Price (UMP). The LMP and UMP were obtained by solving robust unit commitment and security-constrained economic dispatch, representing the need for flexibility resources. Second, the optimal operational strategy of MESs was established to respond to LMP and UMP and maximize their profits by providing energy and reserve flexibility subjects to the reserve and traffic constraints. Third, a game-theoretic model was developed to determine market equilibrium by minimizing the operational costs of the power system and maximizing the profits of MES owners. To avoid homogenous behaviors of MESs in solving this model, a sequential dispatching algorithm was developed such that each MES of one MES owner has a unique price signal. An objective function update strategy was accordingly developed to take the interaction among MESs into consideration and ensure a maximum total profit for MES owners. Finally, case studies with IEEE 6-bus system, IEEE 118-bus system, and MATPOWER 300-bus system were provided to validate the proposed methods, demonstrating that MESs increase power system flexibility and their own profits while decreasing the energy and reserve payment of consumers. • Mobile energy storage has temporal, spatial, and power/energy flexibility. • We provide a market-based methodology to incent mobile energy storage to provide flexibility. • Efficient algorithm is developed to obtain the market equilibrium. • Flexibility provided by mobile energy storages reduces the operational cost of power systems. • Mobile energy storage owners obtain revenue by providing flexibility service. [ABSTRACT FROM AUTHOR]