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doi: 10.3934/jimo.2021147
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B2C online ride-hailing pricing and service optimization under competitions

1. 

School of Management, Jiangsu University, Zhenjiang, 212013, China

2. 

School of Management, Guangzhou University, Guangzhou, 510006, China

* Corresponding author: Changzhi Wu

Received  February 2021 Revised  June 2021 Early access August 2021

B2C online ride-hailing is to provide customers with anytime, anywhere and on-call ride services by professional vehicles and professional drivers. How to maintain good service quality and reasonable pricing under competition is of importance to a platform. In this paper, we will integrate pricing and service together to maximize the profit of a platform through Nash game theory. Specifically, we will establish the models for there scenarios: the demand market competition under decline of ride demand, the supply market competition under surge of ride demand, and the coexistence of demand and supply market competition for stable ride demand. Then, the Nash equilibriums are derived for the three models which are corresponding to minimize ride price, optimize quality of efforts and maximize profit. Our results uncover that the driver's incentive amount is conducive to the profit of both platform and the drivers for the case of demand market competition. The platforms and drivers achieve the highest profit under supply market competition, and the strategy through minimizing price and maximizing service can effectively adjust the balance between market supply and demand.

Citation: Qingfeng Meng, Wenjing Li, Zhen Li, Changzhi Wu. B2C online ride-hailing pricing and service optimization under competitions. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021147
References:
[1]

M. N. Almunawar, M. Anshari and S. A. Lim, Customer acceptance of ride-hailing in Indonesia, Journal of Science and Technology Policy Management, 2021 (2021). Google Scholar

[2]

P. Belleflamme and M. Peitz, Platform competition: Who benefits from multihoming?, International Journal of Industrial Organization, 64 (2019), 1-26.  doi: 10.1016/j.ijindorg.2018.03.014.  Google Scholar

[3]

B. BaiZ. GuoC. ZhouW. Zhang and J. Zhang, An application of adaptive reliability importance sampling-based extended Domain PSO on single mode failure in reliability engineering, Inform. Sci., 546 (2021), 42-59.  doi: 10.1016/j.ins.2020.07.069.  Google Scholar

[4]

J. R. BaiK. C. SoC. S. TangX. Chen and H. Wang, Coordinating supply and demand on an on-demand service platform with impatient customers, M & Som-Manufacturing and Service Operations Management, 21 (2019), 479-771.  doi: 10.1287/msom.2018.0707.  Google Scholar

[5]

K. BimpikisO. Candogan and D. Saban, Spatial pricing in ride-sharing networks, Oper. Res., 67 (2019), 599-904.  doi: 10.1287/opre.2018.1800.  Google Scholar

[6]

G. P. CachonK. M. Daniels and R. Lobel, The role of surge pricing on a service platform with self-scheduling capacity, Sharing Economy, 6 (2015), 101-113.  doi: 10.1007/978-3-030-01863-4_6.  Google Scholar

[7]

J. P. Choi and Y. Zennyo, Platform market competition with endogenous side decisions, Journal of Economics and Management Strategy, 28 (2019), 73-88.  doi: 10.1111/jems.12305.  Google Scholar

[8]

J. Correia-da-SilvaB. JullienY. Lefouili and J. Pinho, Horizontal mergers between multisided platforms: Insights from cournot competition, Journal of Economics and Management Strategy, 28 (2019), 109-124.  doi: 10.1111/jems.12309.  Google Scholar

[9]

H. ChenH. QiaoL. XuQ. Feng and K. Cai, A fuzzy optimization strategy for the implementation of RBF LSSVR model in Vis-NIR analysis of pomelo maturity, IEEE Transactions on Industrial Informatics, 15 (2019), 5971-5979.  doi: 10.1109/TII.2019.2933582.  Google Scholar

[10]

L. DingS. LiH. GaoC. Chen and Z. Deng, Adaptive partial reinforcement learning neural network-based tracking control for wheeled mobile robotic systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50 (2020), 2512-2523.  doi: 10.1109/TSMC.2018.2819191.  Google Scholar

[11]

Q. Dong and L. Cui, Reliability analysis of a system with two-stage degradation using wiener processes with piecewise linear drift, IMA J. Manag. Math., 32 (2021), 3-29.  doi: 10.1093/imaman/dpaa009.  Google Scholar

[12]

L. DingS. LiH. GaoC. Chen and Z. Deng, Adaptive neural network-based finite-time online optimal tracking control of the nonlinear system with dead zone, IEEE Transactions on Cybernetics, 51 (2019), 382-392.   Google Scholar

[13]

G. A. Daniel, Cybersecurity and platform competition in the cloud, Computers and Security, 93 (2020), 101774. Google Scholar

[14]

Y. GuoX. T. Li and X. H. Zeng, Platform competition in the sharing economy: Understanding how ride-hailing services influence new car purchases, Journal of Management Information Systems, 36 (2019), 1043-1070.  doi: 10.1080/07421222.2019.1661087.  Google Scholar

[15]

E. Gal-Or, R. Gal-Or and N. Penmetsa, Can platform competition support market segmentation? Network externalities versus matching efficiency in equity crowdfunding markets, Journal of Economics and Management Strategy, 28 (2019), 420-435. doi: 10.1111/jems.12286.  Google Scholar

[16]

Y. M. Gui and B. G. Gong, Quality assurance competition strategy under B2C platform, Discrete Dyn. Nat. Soc., 2016 (2016), 1-5.  doi: 10.1155/2016/6587872.  Google Scholar

[17]

X. HuH. Y. Chong and X. Wang, Sustainability perceptions of off-site manufacturing stakeholders in Australia, Journal of Cleaner Production, 227 (2019), 346-354.  doi: 10.1016/j.jclepro.2019.03.258.  Google Scholar

[18]

H. Halaburda and Y. Yehezkel, The role of coordination bias in platform competition, Journal of Economics and Management Strategy, 25 (2016), 274-312.  doi: 10.2139/ssrn.2164339.  Google Scholar

[19]

Y. Jin and Y. L. Zhang, An analysis of the impact of shopping environment on trading in price competition of retail platform, Basic and Clinical Pharmacology and Toxicology, 126 (2020), 336-337.   Google Scholar

[20]

T. D. Jeitschko and M. J. Tremblay, Platform competition with endogenous homing, Internat. Econom. Rev., 61 (2020), 1281-1305.  doi: 10.1111/iere.12457.  Google Scholar

[21]

J. J. LiuC. Z. WuG. N. Wu and x. y. Wang, A novel differential search algorithm and applications for structure design, Applied Mathematics and Computation, 268 (2020), 246-269.  doi: 10.1016/j.amc.2015.06.036.  Google Scholar

[22]

S. LiuF. Chan and W. Ran, Decision making for the selection of cloud vendor: An improved approach under group decision-making with integrated weights and objective/subjective attributes, Expert Systems with Applications, 55 (2016), 37-47.  doi: 10.1016/j.eswa.2016.01.059.  Google Scholar

[23]

S. LiuW. YuF. Chan and B. Niu, A variable weight-based hybrid approach for multi-attribute group decision making under interval-valued intuitionistic fuzzy sets, International Journal of Intelligent Systems, 36 (2021), 1015-1052.   Google Scholar

[24]

L. Liu and L. Sen, Integrated production and distribution problem of perishable products with a minimum total order weighted delivery time, Mathematics, 8 (2020), 146. doi: 10.3390/math8020146.  Google Scholar

[25]

P. MaH. Y. Wang and J. Shang, Supply chain channel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581.  doi: 10.1016/j.ijpe.2013.04.020.  Google Scholar

[26]

R. de MattaT. J. Lowe and D. F. Zhang, Competition in the multi-sided platform market channel, International Journal of Production Economics, 182 (2017), 40-51.  doi: 10.1016/j.ijpe.2017.03.022.  Google Scholar

[27]

X. Peng and H. Tian-run, Optimal quality effort strategy in O2O food delivery service supply chain based on three operation models, Technology Analysis and Strategic Management, 28 (2020), 115-126.   Google Scholar

[28]

G. Papachristos and V. D. K. Geerten, Understanding platform competition through simulation: A research outline, Technology Analysis and Strategic Management, 30 (2018), 1409-1421.  doi: 10.1080/09537325.2018.1473850.  Google Scholar

[29]

W. RanS. Liu and Z. Zhang, Polling-based dynamic Order-picking system considering priority orders, Complexity, 3 (2020), 1-15.   Google Scholar

[30]

J. RenC. Zhang and Q. Hao, A theoretical method to evaluate honeynet potency, Future Generation Computer Systems, 116 (2021), 76-85.   Google Scholar

[31]

Z. M. Sun and Q. Xu, Dynamic pricing for ride-hailing platforms with different competition conditions under stochastic demand, Chinese Journal of Management Science, 29 (2021), 1-13.   Google Scholar

[32]

M. Sood, A. A. Kulkarni and S. Moharir, Platform competition for throughput in two-sided freelance markets, in 2018 International Conference on Signal Processing and Communications, (eds. IEEE), Academic Press, (2018), 227–231. doi: 10.1109/SPCOM.2018.8724409.  Google Scholar

[33]

L. Y. SunR. H. TeunterM. Z. Babai and G. W. Hua, Optimal pricing for ride-sourcing platforms, European J. Oper. Res., 278 (2019), 783-795.  doi: 10.1016/j.ejor.2019.04.044.  Google Scholar

[34]

S. Y. WangH. M. Chen and D. S. Wu, Regulating platform competition in two-sided markets under the O2O era, International Journal of Production Economics, 215 (2019), 131-143.  doi: 10.1016/j.ijpe.2017.10.031.  Google Scholar

[35]

C. Z. Wu, X. Y. Wang, M. C. Chen and M. J. Kim, Differential received signal strength based RFID positioning for construction equipment tracking, Advanced Engineering Informatics, 42 (2019), 100960. doi: 10.1016/j.aei.2019.100960.  Google Scholar

[36]

Z. XiongN. XiaoF. XuX. ZhangQ. XuK. Zhang and C. Ye, An equivalent exchange based data forwarding incentive scheme for socially aware networks, Journal of Signal Processing Systems for Signal Image and Video Technology, 93 (2021), 249-263.   Google Scholar

[37]

Y. Xu, X. B. Tao and Y. B. Sun, Study of bilateral trading platform competition in consideration of suppliers' spatial network, International Journal of Modern Physics C, 29 (2018), 1840003. doi: 10.1142/S012918311840003X.  Google Scholar

[38]

C. W. Yan, H. L. Zhu, N. Korolko and D. Woodard, Dynamic pricing and matching in ride-hailing platforms, forthcoming, Naval Research Logistics, 2018, Available from: https://ssrn.com/abstract=3258234 or http://dx.doi.org/10.2139/ssrn.3258234. Google Scholar

[39]

J. Yan, W. Pu, S. Zhou, H. Liu and M. Greco, Optimal resource allocation for asynchronous multiple targets tracking in heterogeneous radar networks, IEEE Transactions on Signal Processing, 68 (2020) 4055–4068. doi: 10.1109/TSP.2020.3007313.  Google Scholar

[40]

H. Yue, H. Wang, H. Chen, K. Cai and Y. Jin, Automatic detection of feather defects using Lie group and fuzzy Fisher criterion for shuttlecock production, Mechanical Systems and Signal Processing, 141 (2020), 106690. doi: 10.1016/j.ymssp.2020.106690.  Google Scholar

[41]

J. ZhuQ. ShiP. WuZ. Sheng and X. Wang, Complexity analysis of prefabrication contractors' dynamic price competition in mega projects with different competition strategies, Complexity, 2018 (2018), 1-9.  doi: 10.1155/2018/5928235.  Google Scholar

[42]

Y. G. ZhongZ. Z. LinY. W. ZhouT. C. E. Cheng and X. G. Lin, Matching supply and demand on ride-sharing platforms with permanent agents and competition, International Journal of Production Economics, 218 (2019), 363-374.  doi: 10.1016/j.ijpe.2019.07.009.  Google Scholar

[43]

B. Zeng, Y. Liu, F. Xu, Y. Liu, X. Sun and X. Ye, Optimal demand response resource exploitation for efficient accommodation of renewable energy sources in multi-energy systems considering correlated uncertainties, Journal of Cleaner Production, 288 (2021). Google Scholar

[44]

L. T. ZhaY. F. Yin and Y. C. Du, Surge pricing and labor supply in the ride-sourcing market, Transportation Research Part B-Methodological, 117 (2018), 708-722.   Google Scholar

[45]

S. Zhong-miao and X. Qi, Dynamic pricing for ride-hailing platforms with different competition conditions under stochastic demand, Chinese Journal of Management Science, 2020 (2020), 1-23.   Google Scholar

[46]

B. Zeng, Y. Liu, F. Xu, Y. Liu and X. Ye, Optimal demand response resource exploitation for efficient accommodation of renewable energy sources in multi-energy systems considering dorrelated uncertainties, Journal of Cleaner Production, 288 (2020), 125666. Google Scholar

show all references

References:
[1]

M. N. Almunawar, M. Anshari and S. A. Lim, Customer acceptance of ride-hailing in Indonesia, Journal of Science and Technology Policy Management, 2021 (2021). Google Scholar

[2]

P. Belleflamme and M. Peitz, Platform competition: Who benefits from multihoming?, International Journal of Industrial Organization, 64 (2019), 1-26.  doi: 10.1016/j.ijindorg.2018.03.014.  Google Scholar

[3]

B. BaiZ. GuoC. ZhouW. Zhang and J. Zhang, An application of adaptive reliability importance sampling-based extended Domain PSO on single mode failure in reliability engineering, Inform. Sci., 546 (2021), 42-59.  doi: 10.1016/j.ins.2020.07.069.  Google Scholar

[4]

J. R. BaiK. C. SoC. S. TangX. Chen and H. Wang, Coordinating supply and demand on an on-demand service platform with impatient customers, M & Som-Manufacturing and Service Operations Management, 21 (2019), 479-771.  doi: 10.1287/msom.2018.0707.  Google Scholar

[5]

K. BimpikisO. Candogan and D. Saban, Spatial pricing in ride-sharing networks, Oper. Res., 67 (2019), 599-904.  doi: 10.1287/opre.2018.1800.  Google Scholar

[6]

G. P. CachonK. M. Daniels and R. Lobel, The role of surge pricing on a service platform with self-scheduling capacity, Sharing Economy, 6 (2015), 101-113.  doi: 10.1007/978-3-030-01863-4_6.  Google Scholar

[7]

J. P. Choi and Y. Zennyo, Platform market competition with endogenous side decisions, Journal of Economics and Management Strategy, 28 (2019), 73-88.  doi: 10.1111/jems.12305.  Google Scholar

[8]

J. Correia-da-SilvaB. JullienY. Lefouili and J. Pinho, Horizontal mergers between multisided platforms: Insights from cournot competition, Journal of Economics and Management Strategy, 28 (2019), 109-124.  doi: 10.1111/jems.12309.  Google Scholar

[9]

H. ChenH. QiaoL. XuQ. Feng and K. Cai, A fuzzy optimization strategy for the implementation of RBF LSSVR model in Vis-NIR analysis of pomelo maturity, IEEE Transactions on Industrial Informatics, 15 (2019), 5971-5979.  doi: 10.1109/TII.2019.2933582.  Google Scholar

[10]

L. DingS. LiH. GaoC. Chen and Z. Deng, Adaptive partial reinforcement learning neural network-based tracking control for wheeled mobile robotic systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50 (2020), 2512-2523.  doi: 10.1109/TSMC.2018.2819191.  Google Scholar

[11]

Q. Dong and L. Cui, Reliability analysis of a system with two-stage degradation using wiener processes with piecewise linear drift, IMA J. Manag. Math., 32 (2021), 3-29.  doi: 10.1093/imaman/dpaa009.  Google Scholar

[12]

L. DingS. LiH. GaoC. Chen and Z. Deng, Adaptive neural network-based finite-time online optimal tracking control of the nonlinear system with dead zone, IEEE Transactions on Cybernetics, 51 (2019), 382-392.   Google Scholar

[13]

G. A. Daniel, Cybersecurity and platform competition in the cloud, Computers and Security, 93 (2020), 101774. Google Scholar

[14]

Y. GuoX. T. Li and X. H. Zeng, Platform competition in the sharing economy: Understanding how ride-hailing services influence new car purchases, Journal of Management Information Systems, 36 (2019), 1043-1070.  doi: 10.1080/07421222.2019.1661087.  Google Scholar

[15]

E. Gal-Or, R. Gal-Or and N. Penmetsa, Can platform competition support market segmentation? Network externalities versus matching efficiency in equity crowdfunding markets, Journal of Economics and Management Strategy, 28 (2019), 420-435. doi: 10.1111/jems.12286.  Google Scholar

[16]

Y. M. Gui and B. G. Gong, Quality assurance competition strategy under B2C platform, Discrete Dyn. Nat. Soc., 2016 (2016), 1-5.  doi: 10.1155/2016/6587872.  Google Scholar

[17]

X. HuH. Y. Chong and X. Wang, Sustainability perceptions of off-site manufacturing stakeholders in Australia, Journal of Cleaner Production, 227 (2019), 346-354.  doi: 10.1016/j.jclepro.2019.03.258.  Google Scholar

[18]

H. Halaburda and Y. Yehezkel, The role of coordination bias in platform competition, Journal of Economics and Management Strategy, 25 (2016), 274-312.  doi: 10.2139/ssrn.2164339.  Google Scholar

[19]

Y. Jin and Y. L. Zhang, An analysis of the impact of shopping environment on trading in price competition of retail platform, Basic and Clinical Pharmacology and Toxicology, 126 (2020), 336-337.   Google Scholar

[20]

T. D. Jeitschko and M. J. Tremblay, Platform competition with endogenous homing, Internat. Econom. Rev., 61 (2020), 1281-1305.  doi: 10.1111/iere.12457.  Google Scholar

[21]

J. J. LiuC. Z. WuG. N. Wu and x. y. Wang, A novel differential search algorithm and applications for structure design, Applied Mathematics and Computation, 268 (2020), 246-269.  doi: 10.1016/j.amc.2015.06.036.  Google Scholar

[22]

S. LiuF. Chan and W. Ran, Decision making for the selection of cloud vendor: An improved approach under group decision-making with integrated weights and objective/subjective attributes, Expert Systems with Applications, 55 (2016), 37-47.  doi: 10.1016/j.eswa.2016.01.059.  Google Scholar

[23]

S. LiuW. YuF. Chan and B. Niu, A variable weight-based hybrid approach for multi-attribute group decision making under interval-valued intuitionistic fuzzy sets, International Journal of Intelligent Systems, 36 (2021), 1015-1052.   Google Scholar

[24]

L. Liu and L. Sen, Integrated production and distribution problem of perishable products with a minimum total order weighted delivery time, Mathematics, 8 (2020), 146. doi: 10.3390/math8020146.  Google Scholar

[25]

P. MaH. Y. Wang and J. Shang, Supply chain channel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581.  doi: 10.1016/j.ijpe.2013.04.020.  Google Scholar

[26]

R. de MattaT. J. Lowe and D. F. Zhang, Competition in the multi-sided platform market channel, International Journal of Production Economics, 182 (2017), 40-51.  doi: 10.1016/j.ijpe.2017.03.022.  Google Scholar

[27]

X. Peng and H. Tian-run, Optimal quality effort strategy in O2O food delivery service supply chain based on three operation models, Technology Analysis and Strategic Management, 28 (2020), 115-126.   Google Scholar

[28]

G. Papachristos and V. D. K. Geerten, Understanding platform competition through simulation: A research outline, Technology Analysis and Strategic Management, 30 (2018), 1409-1421.  doi: 10.1080/09537325.2018.1473850.  Google Scholar

[29]

W. RanS. Liu and Z. Zhang, Polling-based dynamic Order-picking system considering priority orders, Complexity, 3 (2020), 1-15.   Google Scholar

[30]

J. RenC. Zhang and Q. Hao, A theoretical method to evaluate honeynet potency, Future Generation Computer Systems, 116 (2021), 76-85.   Google Scholar

[31]

Z. M. Sun and Q. Xu, Dynamic pricing for ride-hailing platforms with different competition conditions under stochastic demand, Chinese Journal of Management Science, 29 (2021), 1-13.   Google Scholar

[32]

M. Sood, A. A. Kulkarni and S. Moharir, Platform competition for throughput in two-sided freelance markets, in 2018 International Conference on Signal Processing and Communications, (eds. IEEE), Academic Press, (2018), 227–231. doi: 10.1109/SPCOM.2018.8724409.  Google Scholar

[33]

L. Y. SunR. H. TeunterM. Z. Babai and G. W. Hua, Optimal pricing for ride-sourcing platforms, European J. Oper. Res., 278 (2019), 783-795.  doi: 10.1016/j.ejor.2019.04.044.  Google Scholar

[34]

S. Y. WangH. M. Chen and D. S. Wu, Regulating platform competition in two-sided markets under the O2O era, International Journal of Production Economics, 215 (2019), 131-143.  doi: 10.1016/j.ijpe.2017.10.031.  Google Scholar

[35]

C. Z. Wu, X. Y. Wang, M. C. Chen and M. J. Kim, Differential received signal strength based RFID positioning for construction equipment tracking, Advanced Engineering Informatics, 42 (2019), 100960. doi: 10.1016/j.aei.2019.100960.  Google Scholar

[36]

Z. XiongN. XiaoF. XuX. ZhangQ. XuK. Zhang and C. Ye, An equivalent exchange based data forwarding incentive scheme for socially aware networks, Journal of Signal Processing Systems for Signal Image and Video Technology, 93 (2021), 249-263.   Google Scholar

[37]

Y. Xu, X. B. Tao and Y. B. Sun, Study of bilateral trading platform competition in consideration of suppliers' spatial network, International Journal of Modern Physics C, 29 (2018), 1840003. doi: 10.1142/S012918311840003X.  Google Scholar

[38]

C. W. Yan, H. L. Zhu, N. Korolko and D. Woodard, Dynamic pricing and matching in ride-hailing platforms, forthcoming, Naval Research Logistics, 2018, Available from: https://ssrn.com/abstract=3258234 or http://dx.doi.org/10.2139/ssrn.3258234. Google Scholar

[39]

J. Yan, W. Pu, S. Zhou, H. Liu and M. Greco, Optimal resource allocation for asynchronous multiple targets tracking in heterogeneous radar networks, IEEE Transactions on Signal Processing, 68 (2020) 4055–4068. doi: 10.1109/TSP.2020.3007313.  Google Scholar

[40]

H. Yue, H. Wang, H. Chen, K. Cai and Y. Jin, Automatic detection of feather defects using Lie group and fuzzy Fisher criterion for shuttlecock production, Mechanical Systems and Signal Processing, 141 (2020), 106690. doi: 10.1016/j.ymssp.2020.106690.  Google Scholar

[41]

J. ZhuQ. ShiP. WuZ. Sheng and X. Wang, Complexity analysis of prefabrication contractors' dynamic price competition in mega projects with different competition strategies, Complexity, 2018 (2018), 1-9.  doi: 10.1155/2018/5928235.  Google Scholar

[42]

Y. G. ZhongZ. Z. LinY. W. ZhouT. C. E. Cheng and X. G. Lin, Matching supply and demand on ride-sharing platforms with permanent agents and competition, International Journal of Production Economics, 218 (2019), 363-374.  doi: 10.1016/j.ijpe.2019.07.009.  Google Scholar

[43]

B. Zeng, Y. Liu, F. Xu, Y. Liu, X. Sun and X. Ye, Optimal demand response resource exploitation for efficient accommodation of renewable energy sources in multi-energy systems considering correlated uncertainties, Journal of Cleaner Production, 288 (2021). Google Scholar

[44]

L. T. ZhaY. F. Yin and Y. C. Du, Surge pricing and labor supply in the ride-sourcing market, Transportation Research Part B-Methodological, 117 (2018), 708-722.   Google Scholar

[45]

S. Zhong-miao and X. Qi, Dynamic pricing for ride-hailing platforms with different competition conditions under stochastic demand, Chinese Journal of Management Science, 2020 (2020), 1-23.   Google Scholar

[46]

B. Zeng, Y. Liu, F. Xu, Y. Liu and X. Ye, Optimal demand response resource exploitation for efficient accommodation of renewable energy sources in multi-energy systems considering dorrelated uncertainties, Journal of Cleaner Production, 288 (2020), 125666. Google Scholar

Figure 1.  The operation process of the online ride-hailing platform
Figure 2.  The influence of the upper limit of driver's incentive amount on the optimal strategy
Figure 3.  The influence of the upper limit of driver's incentive amount on the optimal profit
Figure 4.  The influence of ride demand market competition on the optimal price change trajectory
Figure 5.  The influence of ride demand market competition on the optimal platform service change trajectory
Figure 6.  The influence of ride demand market competition on the optimal drives service change trajectory
Figure 7.  The influence of market competition of ride demand on the optimal profit change trajectory
Table 1.  Variable description
Variable Variable description
$ p_j $ The ride price of online ride-hailing platform in the $ j $-th model
$ s_{1j} $ The quality of service effort of the online ride-hailing platform in the $ j $-th mdel
$ s_{2j} $ The quality of service efforts of the driver in the $ j $-th mdel
$ j $ $ j=l,u,b $ represent the demand market competition, the supply market completion, and the coexistence of demand and supply market competition, respectively
$ c $ The unit operating costs of the B2C online ride-hailing platforms
$ m $ The fixed delivery cost for drivers
$ D_0 $ The initial market ride demand
$ a $ The market ride demand fluctuation factor
$ q_1 $ The cost of platform unit quality of service improvement
$ q_2 $ The cost of driver unit quality of service improvement
$ M_1 $ The fixed development and operation costs of B2C online ride-hailing platform
$ M_2 $ The fixed training and management costs for drivers
$ \theta $ The ride price sensitivity coefficient
$ \beta $ The sensitivity coefficient of quality of service efforts of B2C online ride-hailing platforms and drivers
$ k_D $ The ride demand market competition coefficient
$ \lambda $ The incentive upper limit of drivers
$ \pi_{1j} $ The profit of the B2C online ride-hailing platforms respectively in the $ j $-th model
$ \pi_{2j} $ The profit of the drivers in the $ j $-th model
$ superscript^* $ The optimal variable value
$ p_j^* $, $ \pi_{1j}^* $, $ \pi_{2j}^* $ The optimal decision variable value
Variable Variable description
$ p_j $ The ride price of online ride-hailing platform in the $ j $-th model
$ s_{1j} $ The quality of service effort of the online ride-hailing platform in the $ j $-th mdel
$ s_{2j} $ The quality of service efforts of the driver in the $ j $-th mdel
$ j $ $ j=l,u,b $ represent the demand market competition, the supply market completion, and the coexistence of demand and supply market competition, respectively
$ c $ The unit operating costs of the B2C online ride-hailing platforms
$ m $ The fixed delivery cost for drivers
$ D_0 $ The initial market ride demand
$ a $ The market ride demand fluctuation factor
$ q_1 $ The cost of platform unit quality of service improvement
$ q_2 $ The cost of driver unit quality of service improvement
$ M_1 $ The fixed development and operation costs of B2C online ride-hailing platform
$ M_2 $ The fixed training and management costs for drivers
$ \theta $ The ride price sensitivity coefficient
$ \beta $ The sensitivity coefficient of quality of service efforts of B2C online ride-hailing platforms and drivers
$ k_D $ The ride demand market competition coefficient
$ \lambda $ The incentive upper limit of drivers
$ \pi_{1j} $ The profit of the B2C online ride-hailing platforms respectively in the $ j $-th model
$ \pi_{2j} $ The profit of the drivers in the $ j $-th model
$ superscript^* $ The optimal variable value
$ p_j^* $, $ \pi_{1j}^* $, $ \pi_{2j}^* $ The optimal decision variable value
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