This paper presents a multi-objective two-stage bilevel stochastic programming framework for a dominant electricity producer to determine an optimal trading strategy in a deregulated electricity spot market in a medium-term time horizon: at the first stage and upper level, the dominant producer aims at maximizing its expected market share and profit, while taking into account the trade-off between the two objectives, and at the second stage and lower level, the independent system operator determines the dispatches and power flows on an hourly basis after realization of uncertainty in market demand, by solving an optimization problem which aims at maximizing the total social welfare. Through Karush–Kuhn–Tucker conditions, the lower level problem is formulated as a complementarity problem and subsequently the dominant producer’s optimal decision making problem as a two-stage stochastic mathematical problem with equilibrium constraints (SMPEC). To solve the SMPEC, it is proposed to reformulate the SMPEC as a mixed integer linear program by representing the complementarity constraints as a system of mixed integer linear inequalities with binary variables. Numerical tests results are reported through a medium size case study based on Italian electricity market.