考虑消费者预期的电动汽车分时租赁市场价格竞争模型

分时租赁平台作为电动汽车推广的主要方式，其特征与打车软件类似，在风险资本的推动下极易引发价格战。各租车公司的市场需求量不仅与自己的定价有关，也与竞争对手的定价策略相关，目标都是各自利润的最大化。本文在考虑消费者预期的基础上，研究了需求函数为线性情形下的多人博弈，证明了此博弈是超模博弈以及Nash均衡的存在性和唯一性。并进一步揭示了降价幅度、交叉价格和价格敏感消费群体占比对均衡价格、均衡需求量和利润的影响关系，讨论了价格竞争过程中各租车公司的决策过程与利弊关系。结果表明：任意租车公司的降价行为都会引发整个市场的降价反应，且降价幅度随着博弈阶段的推进逐渐减小，最终收敛于均衡价格；动态定价博弈存在最优组合策略，市场竞争时应当把握好降价幅度，避免过度的价格竞争；均衡价格是关于消费者预期的单调减函数，价格敏感的消费群体占比越大，租车公司间价格竞争越激烈，降价幅度会越大，均衡价格越低；对于市场份额大的租车公司利润是关于价格敏感型消费者占比的单调增函数，但对中小租车公司而言则是单调减函数，价格敏感的消费者越多，对大公司有利，对中小公司不利。

Price Competition Game among Electric Vehicle Rental Companies Considering Consumer Anticipation

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.