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Forward contracts play an important role for market power mitigation and risk hedging in electricity markets. In this paper, a two-settlement electricity market including a forward market and a spot market is formulated as a two-stage game. The linear supply function equilibrium (LSFE) model and Cournot model are used to model strategic bidding for the spot market, while the forward market is modeled by Cournot model. A coevolutionary genetic algorithm (CGA) is employed to determine the market equilibrium. The paper then examines the question whether generation companies (GenCos) would voluntarily enter forward markets due to economic inspiration and studies theoretically and numerically the factors which can affect the bidding behaviors of GenCos. The effectiveness of CGA in determining the market equilibrium is investigated and demonstrated based on two test examples. The studies show that GenCos' decisions on the participation in forward markets depend significantly on the type of competition that they have in the spot market. Moreover, GenCos' bidding behaviors in the forward market can be affected by their cost parameters and the slope of system demand function significantly.