In electricity markets, bilateral contracts (BC) are used to hedge against price volatility in the spot market. Pricing these contracts requires scheduling from either the buyer or the seller aiming to achieve the highest profit possible. Since this problem includes different players, a Generation Company (GC) and an Electricity Supplier Company (ESC) are considered. The approaches to solve this problem include the Nash Bargaining Solution (NBS) equilibrium and the Raiffa–Kalai–Smorodinsky (RKS) bargaining solution. The innovation of this work is the implementation of an algorithm based on the RKS equilibrium to find a compromise strategy when determining the concessions to be made by the parties. The results are promising and show that the RKS approach can obtain better results compared to the Nash equilibrium method applied to a case study.