At present Cournot model is one of the most commonly used theories to analyze the gaming situation in oligopoly market. But there exist several problems to apply this model to electricity market. The representative one is to obtain the inverse demand curve able to be induced from the relationship between market price and demand response. In Cournot model, each player offers their generation quantity to accomplish maximum profit, which is accomplished by reducing their quantity compared with available total capacity. As stated above, to obtain the probable Cournot equilibrium to reflect real market situation, we have to induce the correct demand function first of all. Usually the correlation between price and demand appears on the long-term basis through the statistical data analysis (for example, regression analysis) or by investigating consumer utility functions of several consumer groups classified as residential, industrial, and commercial. However, the elasticity has a tendency to change continuously according to the total market demand size or the level of market price. Therefore it should be updated as trading period passes by. In this paper we propose a method for inducing and updating this price elasticity of demand function for more realistic market equilibrium.