This paper presents a new approach for determining the day-ahead bidding strategies of a large-scale hybrid electric energy company. The company has both energy generation and energy retailing businesses in a competitive electricity market. Demand response programs are also considered in the retail side of the company in order to hedge the risk of participation in wholesale market. This paper introduces a max-min bilevel mathematical programming with equilibrium constraint model for offering a strategy that manages the risk of uncertain forecasted rivals' bids by robust optimization. The max-min bilevel model is converted to its equivalent single-level optimization using Karush-Kuhn-Tucker optimality conditions. The duality theory is utilized to find the equivalent ordinary maximization model of the max-min problem. Strong duality theory and big M method are also used to linearize the final model of offering strategy. Applicability of the proposed approach is shown by implementing it on the IEEE 118-bus test system.