In this paper,the authors discuss water supply enterprises cooperative and non-cooperative action of innovation in duopoly market with game theory,and also interpret the microcosmic game mechanism which have explained whether innovation would occur.

Based on a vertical product differentiation model with nonlinear demand function s, the evolutionary stable strategy (ESS) in a duopolistic market in which a hig h quality firm and a low quality firm are involved is studied.

Based on a vertical product differentiation model with linear demand functions, we study the Evolutionary Stable Strategy (ESS) in a duopolistic market in which there are a high quality firm and a low quality firm.

Based on a three-stage Hotelling model, we study the evolutionary stable problem of price strategies in duopolistic retailing market.

The perceptions of the competition trend in the space oligopoly market from M&A;

According to the difficulties when analyzing the oligopoly market theory.

The same project is owned by several enterprises in oligopoly market, and the share of the project will lead to competition.

And the market of new products can be seemed as an oligarch market.

For oligarch market,Cournot game models between two supply chains under symmetric information and asymmetric information are built,in which the corresponding results and relevant explanation have been shown at last.