In this paper, a two-dimensional Cournot model is proposed to study generation companies’ (GENCO’s) strategic quantity-setting behaviors in the newly established Yunnan’s electricity market. A hybrid pricing mechanism is introduced to Yunnan’s electricity market with the aim to stimulate electricity demand. Market equilibrium is obtained by iteratively solving each GENCO’s profit maximization problem and finding their optimal bidding outputs. As the market mechanism is a key element of the electricity market, impacts of different market mechanism parameters on electricity price and power generation in market equilibrium state should be fully assessed. Therefore, based on the proposed model, we precisely explore the impacts on market equilibrium of varying parameters such as the number of GENCOs, the quantity of ex-ante obligatory-use electricity contracts (EOECs) and the elasticity of demand. Numerical analysis results of Yunnan’s electricity market show that these parameters have notable but different effects on electricity price. A larger number of GENCOs or less EOEC contracted with GENCOs will have positive effects on reducing the price. With the increase of demand elasticity, the price falls first and then rises. Comparison of different mechanisms and relationship between different parameters are also analyzed. These results should be of practical interest to market participants or market designers in Yunnan’s or other similar markets.