Abstract: Based on the traits of bounded rationality, imitation as well as learning and improvement exists in the "Internet plus Periodic Renting" market competition. In this paper, an evolutionary game model is construted to reveal the mechanism of the car rental company to grab market share. Specifically, recent phenomenon of Price War in taxi-hailing app market is incorporated to analysis the model. A case study is given to demonstrate the interrelationships among action, evolutionary path and evolutionary stable strategy (ESS) in the end. The research shows that there is no pure strategy evolutionarily stable strategy, when the market is under the impact of price war lunched by a company. However, there must be an evolutionary stable state of the hybrid strategy. For companies that are ready to enter the market or want to expand their market share, the best strategy is to lunch a price war. And for companies that are already operating in the market, the best responsive strategy is to cut price.Theoretical explanation is given for the existence of ESS in car-sharing market competition, which offers guaidance on pricing strategy of the car rental company.

Key words: new-energy vehicles, periodic renting, taxi-hailing apps, market competition, evolutionary game theory