A Bi-level gaming programming for regional integrated energy system considering the users’ reliability incentive

•User reliability incentive is proposed to realize reliability service differentiation.•A master-followers bi-level model is proposed for decision making of operator and users.•Reliability constraint is adjusted considering building thermal inertia and user's status.•The consumptive ability for renewable energy would also be promoted.•The utility in a society-wide is maximized with limited reliability resources.