Abstract: The purpose of establishing the electric vehicle rental market is to let consumers better understand the electric vehicle and solve the contradiction between supply and demand of electric vehicle in the short term. China began to subsidize new energy vehicles in 2010, and began to reduce taxes and fees in 2012. With the increase of government support, the automobile manufacturer has begun to produce electric vehicles on a large scale. However, due to the concerns of high purchase cost, battery safety and mileage, the consumer purchase rate remained at a lower level. Therefore, the automobile manufacturers setting up car rental companies to solve the short-term sales problems, so as to let consumers know more about electric vehicles. And this way of promotion has been positively responded by the market. But with the increasing number of participants, price competition is inevitable in order to compete for market share. Then, what are the optimal strategies for each participant in the competition? What is the equilibrium of game? These issues have aroused attention of both companies and academic researchers.
Unlike general commodities, the electric vehicle rental market is deeply integrated with the Internet, which reduces the information asymmetry between renting businesses and consumers. Therefore, the companies can make more profits by dynamic pricing, and consumers also can make smarter consumer decisions. Some consumers will decide their best consumption opportunity by comparing the utility of consumption under current price conditions with that under future expected price conditions. When they observe a company reducing its price, they expect other companies to follow the price reduction, so they chose to wait. Therefore, it is necessary to take consumer expectations into account when studying price competition game in electric vehicle rental market, a point which has been neglected by previous studies.
Based on the above analysis, a game model, which includes N rental companies, is constructed and the demand of companies is a function of all company prices. And it is assumed that the demand is a decreasing function of its own price and an increasing function of other companies' prices. At the same time, consumer expectations are incorporated into the model, which assumes that some consumer will not consume immediately, but will choose to wait, the proportion of this kind consumers is 1-θ. It is proved that this game is a super modular game that has a unique Nash equilibrium, and the impact of the price cut percentage, crossover price and the proportion of price sensitive consumers on equilibrium price, equilibrium demand quantity and profit are analyzed, so as to depict the complexity relationships between these variables.
The results show that: the price cut behavior of any car rental company will lead to the same reaction of the entire market, and the range of price cut decreases gradually with the advance of the stage game, and eventually converge to the equilibrium price; the dynamic pricing game has an optimal combination strategy. The car rental company should be aware of the range of price cut and avoid excessive price competition; the equilibrium price is the decreasing function of consumers' expectations; the larger part of consumers that are sensitive to prices, the more fierce the competition and the equilibrium price is lower; the profit of large car rental company is the monotone increasing function of price sensitive consumers, and to the small car rental company is monotonous decreasing function. This means that the more price sensitive consumers in the market, the more benefit brought bring about to the big enterprises rather than small and medium-sized enterprises.

Key words: electric vehicle, car-sharing, price competition, supermodular game