In this talk, we focus on a multiobjective problem with equilibrium constraints (MOPEC). This problem has many practical applications in various areas such as energy, environment, health and transportation. We extend the existing MPEC-type constraint qualifications from single objective case to multiobjective case and investigate the relationships among them. Then we derive some stationarity conditions in the proper Pareto sense for MOPEC and, particularly, in order to avoid some objective functions not to play roles, we mainly discuss the proper Pareto stationarity conditions. After that, we propose a partial penalty based proximal alternating linearized minimization algorithm for MOPEC. Some considerations about stochastic multiobjective problem with equilibrium constraints are given at last.