Dynamic Investigations of Shared Bicycle Operators’ Competition Based on Profit Maximization
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper titled "Dynamic Investigations of Shared Bicycle Operators' Competition Based on Profit Maximization" explores the nonlinear dynamics of a duopoly competition between two shared bicycle operators. The research applies the Cournot competition model, focusing on how pricing strategies, discounts, and comfort levels affect demand and profitability. A chaotic attractor specific to the shared bicycle market, termed the "shared bicycle attractor," is discovered, showing how certain operational strategies can lead to chaotic, unsustainable competition.
Technical contributions:
1. Nonlinear duopoly model: The paper constructs a nonlinear Cournot duopoly model to analyze the competition between two bike-sharing operators based on pricing strategies and demand.
2. Profit maximization: The study explores profit maximization through the adjustment of pricing and service quality, incorporating factors such as comfort loss and discounts.
3. Dynamic analysis: Stability analysis of the Cournot competition is performed using the Jacobian matrix and Jury conditions, identifying the equilibrium points and bifurcation behaviors.
4. Chaotic attractor: The discovery of a new chaotic attractor in the shared bicycle market provides insight into how certain strategies can drive the market into chaos, especially when discounting is overly aggressive.
5. Numerical simulations: Simulations using bifurcation diagrams illustrate the sensitivity of the system to initial conditions and the evolution of competition dynamics under various operational adjustments.
Thematic contributions:
1. Shared bicycle market dynamics: The study adds to the growing body of literature on shared transportation by focusing on the market dynamics of the rapidly evolving bike-sharing industry.
2. Impact of discounts and comfort: It highlights how comfort-related costs and discounts can significantly affect market share and long-term sustainability, providing insights for operators on maintaining a competitive edge.
3. Policy recommendations: The results suggest that operators must carefully balance discounts and service improvements to avoid destabilizing the market and introduce potential policy measures to regulate competition.
Technical flaws:
1. Simplification of market factors: While the paper employs a duopoly model, it overlooks other potential market players, such as government regulation, external competition from other modes of transport, or changes in consumer behavior due to environmental factors.
2. Limited scope of parameters: The paper focuses primarily on price and comfort without integrating other important factors like supply chain disruptions, or environmental considerations that may also impact profitability.
Thematic flaws:
1. Narrow focus on duopoly: The focus on a duopoly limits the broader applicability of the findings to real-world scenarios where markets may be more fragmented, with multiple operators and external forces influencing competition.
2. Underrepresentation of consumer preferences: The model mainly considers discounts and comfort but does not fully account for other consumer preferences, such as safety, environmental concerns, or brand loyalty, which might also drive demand.
Room for improvement:
1. Robustness checks: The model could be improved by conducting robustness checks through different market conditions, such as varying the number of competitors, adding government regulations, or analyzing different geographical regions with distinct consumer behaviors.
2. Strategic implications for operators: The findings suggest that excessive discounting may lead to market chaos, but further recommendations could be made regarding alternative strategies, such as diversification, or partnerships with other transportation providers to improve market stability.
3. Extension to network games: The model could be extended to incorporate network game theory, which would allow for a more sophisticated analysis of how shared bicycle operators interact with each other and with other transportation systems. This would make the model more applicable to real-world transportation networks, where competition and collaboration occur not only between direct competitors but also across various modes of transit. For network games, see, for example, Dragicevic, A. (2024), The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph, Bulletin of Mathematical Biology, 86: 69.
Comments on the Quality of English LanguageNo comment.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI have read the article and have some concerns:
1. What gap from the literature covers the paper? I ask the authors to specify it more clearly.
2. I suggest the authors to insert a separate literature review section and present the current state of research.
3. It is not very clear from the article what were the initial data on which the presented model was applied and their source.
4. What version of Mathlab did the authors use to simulate the presented model?
5. I suggest to the authors to insert separate discussion section and discuss the results found.
6. What is the originality of the article?
7. What are the research questions and hypotheses to be answered? I suggest authors to write them in the introduction section.
8. Can the results be extrapolated to any region? Can they be used in other areas?
9. What are the limitations of the study? What is future research?
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThank you for the updates.
Comments on the Quality of English LanguageNo comment.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper can be accepted in the present form.
