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In liberalized electricity markets utilities have incentives to manage their positions in the market and they have considerable interests in making decisions to reduce the risks and modifying several strategies to maximize their profit. In such electricity markets all the participants are responsible for their decisions; therefore various modelling techniques such as optimization, simulation and equilibrium methods are introduced to manage the risks of participating in electricity markets, especially in an environment where participants compete in both spot market bidding and bilateral contract trading. Equilibrium models using a Conjectural Variation (CV) approach to optimize the participants' behaviors in oligopsonistic and oligopolistic market frameworks have been represented in this paper. This conjecture is a belief or estimation of a player, which can be formulized as a rival's sensitivity response to changes in output of each firm. This paper reviews the UK electricity market (BETTA) as a bilateral electricity market structure, analyses the conjectural equilibrium formula for both generation and demand sides of the market also shows how to determine the bilateral market equilibrium point based on Conjectural Variation method and Direct-Search optimization method in a hierarchical algorithm.