# Dynamic Investigations of Shared Bicycle Operators' Competition Based on Profit Maximization
## 1 Introduction  
The integration of shared bicycles with public transportation has effectively addressed unmet travel needs and alleviated the pressure on public transit systems. This service model is particularly important in urban transportation because it provides convenient feeder services from residential areas to main public transit lines, especially where there are large intervals between long-haul transit stations. Research suggests that the development of shared bicycle systems has provided a strong complementary feeder service to public transportation, forming a multilevel and three-dimensional transportation network together with short-distance buses, enhancing the flexibility and efficiency of urban transportation [1]. However, as the market becomes increasingly saturated, competition among shared bicycle operators becomes more intense [2; 3; 4]. To capture a larger market share in the competition and maximize profits, operators need to continuously optimize their operational strategies. Therefore, studying the competitive dynamics among shared bicycle operators is of great significance. The development of the shared bicycle market can be traced back to Europe in 2007, and it rapidly expanded in China. Mobike, Ofo, and other companies have rapidly emerged and obtained a large amount of financing. However, excessive advertising has led to oversupplies in the market, high operating costs, and many companies are facing financial difficulties or even bankruptcy. Currently, the three brands of Meituan Bike, Hello Bike, and Qingju Bike are gradually emerging, forming a three-legged competitive landscape in China. According to the latest market research data, Meituan Bike leads with a selection rate of 64.52%, followed closely by Hello Bike and Qingju Bike with selection rates of 57.32% and 47.22%, respectively [5]. An interesting phenomenon is that between residential areas and the nearest bus or subway stations, there are often only two types of shared bicycles providing services. These two types of shared bicycles are usually affiliated with different operators, and their competition can increase market share, improve service quality, andmay also lead to some market adjustments and optimizations. The existing market players mainly achieve sustainable operation and profit maximization by improving service quality, optimizing scheduling, and reducing operating costs. Profit maximization is one of the fundamental goals of shared bicycle operators and a core concept in microeconomics. According to classical economic theory, businesses adjust the production factors and resource allocation to achieve maximum profits [6]. In the field of shared bicycles, factors affecting profits mainly include the quantity of bicycles deployed, user demand, the maintenance and management costs of the bicycles, pricing strategies, etc. However, excessive competition in quantity may lead to issues such as resource waste, increased pressure on urban management, and a decline in user experience. Scholars and researchers have recognized the issue of rampant competition in the shared bicycle industry and suggested that government oversight and regulatory measures should be employed to curb this excessive rivalry [3; 7; 8]. It appears that a more effective approach might lie in enhancing the self-awareness of companies within the industry to avoid market disorder preemptively, thus preventing the negative consequences that often arise from unbridled competition. This paper assumes that there are only two types of shared bicycles available between residential areas and the nearest subway or bus stations. The main difference between the two types of shared bicycles is their comfort level, such as whether there are insulation pads on the seats. And the operator's revenue only considers self-ticket revenue. An operator is trying to attract more potential users through discounts.