Abstract: With the rapid development of information technology, bike-sharing, which is based on "Internet+" mode, become a best choice for a city to solve the "last kilometer" problem. However, it has also brought a series of public problems due to excessive volume, such as wasting resources and increasing difficult for city management, etc. Thus, how to manage the number of sharing-bike put into the market is very important for both firms who operate bike-sharing business and relevant government departments. To this end, an evolutionary game model is conducted to study the long-term dynamic evolution process of government departments and bike-sharing operators. Results show that, when performance rewards of regulatory is high, the evolutionary equilibrium strategy is regulatory and rational volume. That is, enlargement of supervision strength and punishment strength is helpful to promote bike-sharing operators putting rational volume of bikes into cities and government departments actively regulating the market of bike-sharing. From the perspective of public management, it is necessary for bike-sharing operators to take the social benefits into account when deciding the supply volume of sharing-bike. And the government departments should actively regulate the market, guiding bike-sharing operators to establish an effective market rule.
Then, the evolutionary game model is extended by considering social supervision through social media in which how social media supervision influence the outcome of evolution is discussed. Through analysis of evolution equilibrium strategy, some crucial findings are obtained. Specifically, in addition to increasing performance reward of regulatory and reducing regulatory costs, it is necessary to enlarge the punishment strength for bike-sharing operators who put bikes into market unreasonably and give an effective play to the supervision from social platforms. It increases possibility of realizing a stable market structure with a government that play a role of regulation and bike-sharing operators who can effectively manage the quantity of sharing-bikes.
Above results not only explain why the current market of bike-sharing is falling, but also prove that it is a relatively stable evolutionary trend for government departments to participate in regulation when they consider sharing-bikes as quasi-public products. Additionally, how performance rewards of regulatory, punishment strength, the supervision from social platforms and other factors affect evolution path is clear. Thereby, it provides theoretical basis for bike-sharing operators to response to market changes and government departments to formulate regulatory strategies.

Key words: bike-sharing, quasi-public products, government regulatory, sharing economy